There is a fair amount of case law establishing online businesses as place of public accommodation.
Such lawsuits have been attempted, but AFAIK without success.
https://en.wikipedia.org/wiki/National_Federation_of_the_Bli....
https://www.adatitleiii.com/2012/10/netflix-settles-massachu...
A site that offers games to download can be very accessible but the games themselves might not be and don't have to be; not every product a store sells has to be usable by every potential customer. That's not a reason to not make the site accessible; e.g. a disabled parent should be able to download a game for their non-disabled child.