As suggested by, e.g., the Wikipedia page (or this page at the US Geological Survey), "remote sensing" is used pretty much exclusively for airborne or satellite-based observations of the surface of the Earth (including the ocean floor in some cases).
This makes sense if you consider that "remote" is used in contrast to observations made locally (or "on-site"). E.g., if you walk around on the ground and make observations, those are "local" observations; if you fly a plane and make observations of the same place, those are "remote" observations.
Since astronomical observations are overwhelming of places you simply can't make local observations of, it's unnecessary to specify them as "remote" observations, just as no one call looking up at high-altitude clouds or distant mountain peaks "remote sensing". (And it seems more than a little silly to claim that humans have been doing "remote sensing" for millions of years, even though humans and proto-humans have indeed been looking at the Sun, the Moon, planets, and stars "remotely" for about that long.)
(I have occasionally seen satellite observations of planetary surfaces -- e.g., imaging by probes orbiting Mars -- referred to as a type of remote sensing; this is clearly based on the direct analogy with Earth remote-sensing satellites. But that's about as far as you can push the term.)
You're free to consider astronomy to involve "remote sensing", based on an overly literal and overly logical interpretation of the term, if you like; in practice, no one working in either astronomy or remote sensing does.