Just because they changed some things, they still have to ask for permission, because the base designs are the same on every promo they did. Obviously this isn't a full-on collab, unless they say otherwise, but I'm 100% sure they asked for permission, because that's the way. They could be sued for using RG's templates.
It’s uncertain whether or not YP did ask for permission from Rockstar Games. But because there is no actual mention of Grand Theft Auto, Rockstar Games, or the use of a Rockstar Games logo, it’s unlikely that this is considered to be any kind of collaboration between the two and is enough to prove Rockstar Games doesn’t have anything to do with the album making.
It’s possible for Rockstar Games to sue YP, if they believe both contents are similar enough and said content is being infringed upon. Also, if there is enough confusion to make it seem as if it is a collaboration, that is also enough evidence for a lawsuit.
YP’s team could try and pass it off as a parody, but YP has not only done this with Grand Theft Auto, there is also their ‘YPS’ logo one of of the concept photos that resembles UPS’ logo.