It only sounds nonsensical because of the words in which it's asked. The question raised by anthropic reasoning isn't "why do I live in a time I call the present" (to which, as you say, the answer is linguistic - of course we'd call our time the present) but rather "why do I live in the year 2010?" or, most precisely of all, "Given that I have special access to the subjective experience of one being, why would that be the experience of a being born in the late 20th century, as opposed to some other time?"

That may still sound tautological - after all, if it wasn't the 20th century, it'd be somewhen else and we'd be asking the same question - but in fact it isn't. Consider these two questions:

• Why am I made out of carbon, as opposed to helium?
• Why do I live in the 20th century, as opposed to the 30th?

The correct answer to the second is not saying, "Well, if you were made out of helium, you could just ask why you were made out of helium, so it's a dumb question", it's pointing out the special chemical properties of carbon. Anthropic reasoning suggests that we can try doing the same to point out certain special properties of the 20th century.

The big difference is that the first question can be easily rephrased to "why are people made out of carbon and not of helium", but the second can't. But that difference isn't enough to make the second tautological or meaningless.