Did you, by any chance, had GOG Galaxy installed on your computer (or maybe had some some past GOG Galaxy installation leftovers)?

At the first glimpse, it looks like as if the installer was trying to add the game into a detected GOG Galaxy installation and failed (hence launching GalaxyClient.exe) rather than installing GOG Galaxy itself... Also, game installers for BG2 EE do differ in sizes between "new" and "classic" installers, so what you're reporting shouldn't be the case...

Nevertheless, as I may be wrong and there could be a human error somewhere, I've forwarded this to our Product team to double check everything.

What's your browser version and / or any script-related extensions or userscripts?
It's certainly not as designed, and looks more like a problem on browser side. Especially that at the moment there is no way for 'classic' installers tab to show as default, unless you're using, for example, Adalia Fundamentals.

I managed to reproduce similar issue - not the exact one OP has experienced, but a reverse scenario:

- Going to Account -> Library -> Game [with both installer types]
--- Galaxy installers are shown as default, clicking on a link gives you a *_(g) file
- Switching to Classic installers via 'More..' option:
--- Classic installers message is shown, clicking on a link gives you a normal file
- Closing game view and opening it again (without reloading Library page):
--- Galaxy installers (name + message) are again shown as default *but* clicking on a link will give you a classic file instead

By all accounts it looks like a website glitch, but we are still looking into the problem mentioned by the OP. If any of you guys is able to find the steps to reproduce it then we would be very grateful if you could let us know, for any game.