This is not just some random data fishing result. Even before the results of the two glucosamine papers this year, longevity researcher James Clement wrote in "The Switch", that glucosamine is "an autophagy inducer in a pathway separate fron mTOR-inhibiting." That is big, since autophagy seems to be responsible for most of the benefit from fasting and CR, but almost all autophagy that we know is activated via mTOR.
That means that you have a clear prior that it should increase your healthspan (but as with all autophagy inducers, like resveratrol or cold showers, don't take it after exercise, since it dulls the response). The prior together with the study results working out as expected is a very good sign for a rationalist IMHO.
Unfortunately glucosamine has at least one significant negative effect as well (see e.g examine.com). It is similar to glucose, so can disrupt blood sugar stability.
Our biology is complex. Don't take substances just because of correlations. Strive to know why they work. If you are going to take glucosamine, do it when you want to be catabolic for a while (it has 15h half life), take it together with fat (I have fish oil and quercetin in my notes for reasons I forget - probably blood sugar results from the detailed notes on examine.com) and know if you are in a risk group for diabetes 2, because it might mess slightly with your blood sugar.
The above is from my personal research notes. I don't take glucosamine yet, but believe I will start. I am not a health professional, just a hobbyist.