Do you think we'll ever get a list of what and why certain parts of the world Post Catastrophe stay gamelike and why others shift? Rewatching the anime has me questioning a ton of things, so sorry ahead of time!
Right now, the best answer I can give for why they happen is “the plot demands it,” since Mamare has explicitly stated that there will be some game-like aspects of the world that will never change (I believe weapon handling, i.e. one-handed, two-handed, etc. was one of those things... but then there’s KR).
Some changes I can note, in chronological order:
Effective at the start of the Catastrophe: Specific body parts can be maimed/damaged. No mini-map visualization, skill “hot keys” are shouting the skill names, there is no text chat. Physical body needs have to be met (eating, drinking, going to the bathroom, sleeping). Magical engineering and Real Food Prep are implied to work from the start of the Catastrophe, or at least rather early on. Nureha’s Overlay is discovered from the start (merging skills that normally wouldn’t be merged), I would assume Kanami’s Compression Combo was possible relatively early on as well. You can equip items by picking them up and using them (although if you’re going to do that in an actual battle, make sure they’re character-bound!).
Around three months after the Catastrophe (post-Goblin Raid): Branches, signs, rooftops, other places that could not be walked on in-game can be used as footholds/paths. (So yes, you probably could not jump onto a sign if you wanted to, nor could you run on walls like Souji did in the WWB manga.) More Overskills like Krusty’s Hyperion Eye (affecting one’s own UI) emerge. I would infer that Overskills like Shield Surfing begin working now, in line with the footholds point.
Around five-six months after the Catastrophe (Akiba Raid/Abyssal Shaft): Flavor text becomes real. The world starts expanding. Monsters gain intelligence. People are able to expand their skillsets (like cooking) even without the appropriate subclass. Physical attributes (like voice) and minds are shifting to match the avatar body rather than the person’s real-world body.
Actually, looking at it from this perspective, the greatest number of “un-game-like” changes are in the start of the Catastrophe, but it doesn’t seem that way since a lot of them would be considered a logical progression. It’s only when we get to the Akiba Raid and Abyssal Shaft arcs that there are sudden, glaring changes. I would chalk up the later changes to Empathiom; the world changes according to the increasing amount of Empathiom it absorbs.