I have a fair few square based glasses, it makes no difference I have found on any of them regardless of age they have one thing in common, chips. Something 200 years old will be chipped on a square base unless it's been buried from new or in a museum from new, in my opinion there are too many upper and lower edges and corners not to be damaged. Here is an old glass that has been on here before, a 50's or early 60's wine glass (I would love to know the pattern of as I have a set of six) and a Webbs shot glass from the 80's all chipped in the right places.
The square base has been around for years.
Lovely looking glass John.
Yours could have been tinkered with though, re cut and polished. I see a lot of that in cut glass although the original base would have to have been big in order to polish a chip out, that assuming it had been damaged in the past.
If you look at the edge on the last base picture it looks like 3mm is missing to me on the edge of the tip of the star points?.