I am most definitely checking off circulos-grom5-web.zip for "this file will be played in the browser." HOWEVER I fixed the issue by moving the web zip to the top of the list. So on one hand, problem solved! On the other, this seems like a bug. Thanks for your time!
Edit: That was poorly written! To clarify, the windows version was being chosen because it was at the top of the "Uploads" list on my "Edit Game" page, even when the web version was flagged as the version to use. Moving the flagged web version to the top of Uploads made the game run properly on the page, but it seems like the flag is pretty much ignored in favor of just using the first version on the list.