There is no such thing as "App Store license".

I was referring to the terms and conditions Apple imposes on developers that wish to publish software on the App store.

Luckily you're not required to publish software on the App Store. Many developers sell direct from their website these days.

How is it deliberately incompatible? How is VLC on the app store while claiming in its about page to be GPLv2 licensed? What specific language in the GPL or App Store T&C is incompatible?

You have to declare you own the intellectual rights of the underlying code, a thing GPL does not grant. You can of course dual license your own code but you cannot own code released by someone else under GPL, and you cannot publish it in the App Store. It would be an absolutely trivial change for Apple to make their store friendly towards opens source and there have been multiple protests about this.

I think projects like VLC request some sort of copyright waiver from contributors so they can relicense in the future, or simply ignoring the TOS, and exposing themselves to summary deletion.

There, this explains it, VLC actually is dual licensed under MPLv2 as well according to it’s about page. Thanks for clearing that up