It has to have an x and y velocity. It's just that one of them can be zero. I calculated what they were, and neither was zero.
What do you mean by the start and end of the experiment? The moment the photon leaves one mirror, and the moment it gets to the other?
I'll let t = t1 - t0, x = x1 - x0, and y = y1 - y0, where (x0, y0, t0) marks the start of the experiment and (x1, y1, t1) marks then end. You can't give just the time due to the relativity of simultaneity.
The spacetime interval is zero (it always is with light). So that's sqrt(x^2 + y^2 - t^2) = 0. Setting y to one and solving for x, you get x = sqrt(t^2 - 1). Solving for t = 2, you get x = sqrt(3). This means that, from the point of reference where the light is moving up one meter and horizontally sqrt(3), it takes two meters per c, as opposed to one in the planet's frame. The photon is moving horizontally at the same rate as the planet. Thus, if the planet moves sqrt(3) meters horizontally between the light moving from one mirror to the other, everything takes twice as long as if it doesn't move at all.
You are going to have to set up your problem more rigorously and clear if we are to continue this conversation.
edit: typo
It has been suggested that animals have less subjective experience than people. For example, it would be possible to have an animal that counts as half a human for the purposes of morality. This is an argument as to why that may be the case.
If you're moving away from Earth at 87% of the speed of light, time dilation would make it look like time on Earth is passing half as fast. From your point of reference, everyone will live twice as long. This obviously won't change the number of life years they live. You can't double the amount of good in the world just by moving at 87% the speed of light. It's possible that there's just a preferred point of reference, and everything is based on people's speed relative to that, but I doubt it.
No consider if their brains were slowed down a different way. Suppose you uploaded someone, and made the simulation run at half speed. Would they experience a life twice as long? This seems to be just slowing it down a different way. I doubt it would change the total amount experienced.
If that's true, it means that sentience isn't something you either have or don't have. There can be varying amounts of it. Also, someone whose brain has been slowed down would be less intelligent by most measures, so this is some evidence that subjective experience correlates with intelligence.
Edit: replaced "sentience" with the more accurate "subjective experience".