Isn't that the part that would violate the first sale doctrine?

I think the usual argument is that you don't own the digital good, you have a license to use it, and that license is between you and the originator (or their reseller) directly. And you aren't allowed to resell the license.

E.g. this sort of thing https://www.tomshardware.com/video-games/pc-gaming/steam-che...

No, not if the same itself was unlawful because Alice signed a contract to not sell it like that.

The GPL notably allows for the sale, it was legal here.