Thanks for making the effort to try and understand. You've thrown one more variable into the equation - emotional energy. I don't know if you've considered how these other variables would affect things, but:

Other Variables Involved in Gifted Alienation

Ability to communicate is something that will increase or decrease frustration / alienation / misunderstanding, depending on whether it's low or high. Unfortunately, not all gifted people get the gift of communication, and gifts come in different sizes so they may not get enough of a gift in communication to compensate for the difficulty of communicating ideas and feelings that are as different as theirs.

Age of the person matters a lot. Supposedly, the speed at which you learn doesn't change, but if you're learning at say, twice the average speed, you'll be much further ahead of your age peers at 30 than at 20, and so on. The gap seems to have grown as I have aged (I'm in the ballpark of 30 myself). It has become harder and harder to find stimulating intelligent conversation. Make sure to value your sources of intelligent conversation, you may need them more later on.

Amount of intelligence. If your IQ is 130, you'll notice a difference between yourself and others but if it is over 160, you may feel like a complete alien. One interesting characteristic of the people I've met who have IQs in the profoundly gifted range is that they feel so very different that it's like being stranded on a planet full of aliens. It can be very stressful for them. I don't know what your IQ is, but it sounds to me like you can understand a little bit what this sort of problem would be like for them. You keep saying "need for cognition" but firstly, that's a trait that's more common to gifted people (it fuels the gift!) and not as common to non-gifted people. Secondly, have you ever been asked a lot of "why" questions by a little child and gotten burned out on answering them? Or can you imagine going a year without having a conversation that wasn't one-sided? These are the experiences that some of the very gifted people might have with "need for cognition". It's better if the person wants to know what you have to say, and compensates a little for the difficulty of communication, but it's not a substitute for having a conversation with an intellectual equal.

Also, understanding people's feelings is a lot more complicated than reading faces. If I make a sad face, why did I make a sad face? Is it because someone said something that hurt my ego, and I need a compliment, or is it that the person was trying to hurt my ego, which kicked me in a deeper place - the part of me that questions why I bother to make a difference when the world can be so nasty. I get this kind of misunderstanding a lot. They read my face right, if I show emotion at all (I frequently don't) but they interpret the wrong reasoning into it. People can be particularly stubborn in their interpretations. I can tell them "It's not my ego" and they will insist that it and ignore the real problem. I'm different enough that my explanations sometimes seem unlikely to people, and they disagree with me about my own feelings. I find it intolerable.

If you imagine for a moment that there's a wild variety of people here, all with different amounts of emotional energy, communication ability, different mental age gaps and different IQ gaps. Some of those people will be lucky, like yourself, and have a gap that's not too difficult to overcome considering the communication and emotional resources they have. Others will either have gaps that are much larger than yours, or won't have the same resources to compensate, or both.

Are gifted people more frequently depressed?

As far as whether gifted people are more frequently depressed, this really depends on the source that you read. A lot of things about gifted adults are not well-established. There's not nearly enough research on them, and a lot of published research findings are false. One source of confusion is that there are a lot of prejudiced myths about gifted adults (before Terman did his research, apparently people thought that gifted people were ugly, unhealthy and all kinds of things) so there are studies that refute these myths and do not tell the whole story, and some of the sources disagree on important things. I've read a lot of stuff about gifted adults (I'm a psychology enthusiast and that's my main psychology interest), and here's my take:

For people with IQs under 145, I'd bet that they do have pretty normal rates of depression. For people with IQs over 145, from what I've read, I'd bet that they have elevated rates of existential depression. Whether or not existential depression was lumped in with depression, or did not qualify as depression might be something that influenced the studies you read. For a citation, I will select "Misdiagnosis and Dual Diagnosis of Gifted Children and Adults". Here is an excerpt:

"There is relatively little inherent in being a gifted child or adult that makes them more prone to depression than others. Most often, it is a poor fit between the gifted person and the environment that creates the problems. A lack of understanding and support from teachers, peers, or family can precipitate very real problems of various kinds, including depression. Existential depression is an exception; it seems to emerge in most environments, though some circumstances prompt it more than others. Existential depression is particularly likely among the highly gifted, even though it is not a category of depression that is recognized in the DSM-IV-TR." (Page 133)

Can anything (like intellectual activities) compensate for unmet social needs?

No. If you want a source, I will refer to Mazlow. His hierarchy of needs clearly includes various social needs. Further, his take is that you need to have social needs met before you can actualize your potential. Trying to channel your potential into intellectual activities without having your social needs met is likely to be frustrating. A lot of people (possibly everyone who is not a sociopath?) experience purpose in relation to other humans. This post by Academian explains that experience. The gist of it is: When asking "What is the purpose of life" this question implies a "who" so you need to have agents to have purposes to in order to have a sense of purpose. I experience this need, myself. I need someone to be close to, to have a purpose to. Random strangers and donations are not enough. I am a social organism. I need to bond emotionally with others, to need others, and to be needed by them.

Someone I know with a very high IQ said one key reason he hasn't made anything of his potential is that he has to spend so much time trying to get his social needs met. This is a lot of work - it can be like rebuilding your social life after a move, except imagine that the social life you build never sticks. You'll be constantly rebuilding your social life over and over again. Some people in that range are lucky and meet someone that fulfills their social needs. Others rarely ever find an intellectual equal, let alone one who is compatible with them (even friendship requires a certain amount of compatibility - though this may not be very obvious to people who aren't really different). Some of them try marrying someone that's not an intellectual equal, but the people I know who have tried this struggle with severe depression due to it.

There unfortunately appears to be no substitute for having your social needs met. Therefore, I regard it as important for people who are significantly different (any meaning of different, including different due to having a high IQ) to be able to participate in a haven where they can interact with like minded others without being made to put up with alienation.