I don't see WASM/WebGPU changing anything when it comes to gaming, as an industry, personally. 3d visualizations and interactive websites? Yeah definitely a nice improvement over WebGL 2, if years late. The OP's experience with Adobe is a great example of this.
WebGPU is pretty far behind what AAA games are using even as of 6 years ago. There's extra overhead and security in the WebGPU spec that AAA games do not want. Browsers do not lend themselves to downloading 300gb of assets.
Additionally, indie devs aren't using Steam for the technical capabilities. It's purely about marketshare. Video games are a highly saturated market. The users are all on Steam, getting their recommendations from Steam, and buying games in Steam sales. Hence all the indie developers publish to Steam. I don't see a web browser being appealing as a platform, because there's no way for developers to advertise to users.
That's also only indie games. AAA games use their own launchers, because they don't _need_ the discoverability from being on Steam. So they don't, and avoid the fees. If anything users _want_ the Steam monopoly, because they like the platform, and hate the walled garden launchers from AAA companies.
EDIT: As a concrete example of the type of problem's WASM for games face, see this issue we discovered (can't unload memory after you've loaded it, meaning you can never save memory by dropping the asset data after uploading assets to the GPU, unless you load your assets in a very specific, otherwise suboptimal sequence): https://github.com/bevyengine/bevy/issues/12057#issuecomment...
(I work on high end rendering features for the Bevy game engine https://bevyengine.org, and have extensive experience with WebGPU)