Well, I can't see much of anything (at all in case of the catalog) in IE, so won't bother much. With some quirks in some cases, but it seems like the rest of the web, or at least the sites I go to, can keep working, and definitely at least keep their main functionality, in it, but GOG, a place started as being meant for those interested in older stuff, many likely not thrilled about or even shunning the "modern" trends and products, now wants to be the pinnacle of modern design and web technology use. You'd think at the very least a store would know it's in their best interest to have everyone capable of browsing the products and making purchases. (Actually, since I saw another report of it not working on old FF, wonder if a Palemoon user can say how it fares on that?)
But, yeah, you know what the front page of a store should list? Sales, new releases and (other) news. Having the news there at the bottom, after the list of titles that defaults to the "popular" ones and that nasty and pointless Metro wall of flat "collection" tiles, defeats the purpose of, uh, a front page. As does not having any text show up anymore for news, and needing to click to see past the most recent 3 and be limited to far fewer than before total.
As for that slideshow of enlarging images at the top, with videos starting on hover, what a waste of users' system resources, and bandwidth too for those on capped or slow connections! Was bad enough before, with the slideshow and changing background, now you took that and made it a fair amount worse. And can't even click back/forward through them anymore with arrows it seems, you need to just click on each "tab" there in turn.
As for the store page, yeah, where is the release date filter? Instead of making it more accurate, another thing gone... And what does sorting by oldest and newest do? Output seems to make no sense. And also see no more list of publishers / developers. Was unmanageable before, but should have made it searchable, displaying partial matches during typing, not remove completely and just rely on people knowing they can still just type in search box.
But worst is the lack of even titles anymore. Seriously? Have to hover over each tile in turn to even see the title of the game, there in some small grey on gray, to put it this way, font at the top? And if you do hover you get videos autoplaying? So, in other words, have to put up with autoplay to even see a game's title? And can't search for titles on page for example, since they're not actually there...
Just at a glance, I'm sure others said more and better. Me, won't be bothering much with the site at all under these circumstances. Having to start a secondary browser is not something you do for a site you regularly visit, so forget following releases, likely submitting the covers on MobyGames, maybe some of the editions themselves when they're different, checking nearly any news piece. Not that GOG cares of course, if they did they wouldn't have buried all that.
Oh, and about the privacy concern regarding number of games owned being displayed. Me, don't care, but some do and they don't need to explain why, privacy should be the default, with the right to opt out, not have to opt in. And you can't put the cat back in the bag once some info's out there. There have been screenshots made and posted these days, some pages were likely saved, some information someone didn't want public, and had every right to reasonably expect not to be public again, especially after the first fiasco, got out there and will remain so (albeit accurate only at that time and not in the future) even if it got hidden now.
Otherwise... Lots of empty space, huge things designed for touchscreens, and tiny phone screens, and lots of moving, loading, spinning, magpie-attention-grabbing stuff, and marketing everywhere. Useful information and ease of use, or any concern about users' system resources or bandwidth, what's that? And let's not even mention compatibility with browsers, eh?
