I'm not a legal or IP expert, but the distinction seems clear to me. As I understand it, the poster mentions two cases: publishing the playable game on itch.io and publishing the project source on github. The former sounds fine, using the assets as intended, and if users extract asset from the game they have to have a certain level of savvy and make a deliberate effort (with willful disregard for IP considerations) to dig in and find the assets, and those assets may or may not be easy to identify depending on how much the game engine combines, compresses, and renames in the course of optimization and obfuscation.
The source project, on the other hand, is not a playable product, you are presenting the individual components for building the game in their original form, easily browseable, individually linkable, and downloadable, so that in itself is not much different than just redistributing the files individually or as an assets pack, and making it part of an open source project on github is actually worse since it's easily forkable and cloneable and it's easy to not realize or forget that some of the assets are not intended for redistribution or rationalize that everything in there is open season.
Ultimately, you have to interpret the terms for that asset (Unity's Asset Store license says "integrate it only as incorporated and embedded components of electronic applications and digital media") but I think you also have to consider what the asset vendor would reasonably want. If I was selling game scripts, of course it'd be fine for customers to incorporate them in games, that's the point, and if players extract them and essentially pirate them, that's an unfortunate fact of life, but I wouldn't want customers reposting the files on github or any files server, even within a project, and I don't see why that would be different for models, textures, and sound files.
Just one more example: suppose I wanted to open source my HyperBowl game, which I've stopped developing, so actually I wouldn't mind posting all the Unity scripts I wrote, but if I posted the whole project on github it would include all the art and sound assets which I licensed from the original developer (not to mention all the third-party stuff I got from the Unity Asset Store and other vendors). Even with all the disclaimers, I think that would get me in trouble, even though people have extracted assets from the published game (I recently found one of the soundtracks on youtube with an explanation they pulled it out of my game)