Okay, so I figured out a big part of the problem, but it didn't fix the cursor thing. Something else did, at least as long as I had it running and it's a bit weird.
Long story short: I bought this game with a different email by accident, but I thought I had connected it to my account by logging in afterwards. Apparently this was not the case, even though the record of my buying it is on this account. So I downloaded the demo and that's why the interface was all weird.
But I downloaded the right version from the purchase page link this time and my cursor still didn't show up. I was going to use my snipping tool to send you a video, but then when I had it on... SUDDENLY my cursor was there!
It disappears as soon as my snipping tool is ended, but as long as it's on, the little grabby hand appears. Maybe some issue with the account not being connected to the purchase could've been the problem with downloading, but I don't think it's the problem with the cursor, since I didn't download through itch's app and just did a direct download. It won't even let me download anything other than the demo on the app.
So it's some kind of display thing, that's for sure.