Your answer is telling me that Romer's calculation for speed of light was 220,000 kilometers per second, and today is calculated at 299,792 kilometers per second.
Have no idea what such difference of calculations has to do with observation of images of far away bodies as if they were in their past.
It's a demonstration that the speed of light is finite.
Another one would be laser distance meters, although here we're talking about nanoseconds rather than minutes. Fun fact: Astronomical and earth based measures agree to a high level of accuracy (in fact, the speed of light in air is slightly slower, but earth based measures in an artificial vacuum agree with space-based ones even better).
Given that we know light travels at a finite speed, and given that we know stars are far away, it follows that the light we see left there many years ago.
In fact, the most precise measurement for the distance of nearby stars is through parallax: We use the apparent shift of position caused by the movement of the earth around the sun to determine the stars distance through simple trigonometry. This gives us the stars distance in multiples of the earth-sun-distance. The earth-sun-distance, in turn, is measured by bouncing radio waves off Venus and measuring the time before you receive an echo (you can't bounce radio waves of the sun directly, the signal would be drowned). Then again some simple trigonometry based on the maximal angular distance of Venus and the sun tells you how much further the sun is than Venus.
One consequence of this is that, even if we couldn't measure the speed of light directly and had no idea how to express it in absolute terms as in meters per second, we'd still know that it takes the light from star y x many years to get here - because what we're measuring is its distance in multiples of the time it takes light to go to Venus and back!