cloud game term in this case is more about a game using cloud infrastructure (like flight sim) and not game that you can stream from the cloud, nothing to do with xcloud, psnow or stadia. At least that’s my understanding.
If we assume that this game is real (which pretty likely doesn't, he's working in Death Stranding Director's Cut and happy with Sony and in addition to games wants to make an anime, a movie etc), he was supposed to pitch it to Sony and Stadia before to signing this supposed letter of intention with MS, which means PlayStation and Stadia were supposed to be able to do the game.
Exclusive or not, games on XCloud, PS Now or Stadia are basically normal console/PC games but instead of running on your local console or PC they are running on a console or PC located in a data center. They are normal games. They are very small markets, so it isn't profitable to put there games unless the dev already completed its sales cycle after discounts and so on, or unless getting a serious moneyhatting from the platform holder, case of the Stadia exclusive games or the games that debut day one on Gamepass/XCloud. So it's even less likely to see exclusive games there unless MS or Stadia funds them. Sony won't do it at least for a while because they have a super successful business selling new games and streaming them when old. But XCloud and Stadia will need exclusive games to make their services attractive and to compete with Sony, who is the one who makes more money with business and has the biggest catalog of streamed game exclusives.
There are games, mostly simulators, where their artists instead of drawing the environment art assets from scratch they use as a draft assets satellite info, like the one you get from Google Maps, to make them more 'realistic'. Google Maps and similar are stored in a cloud, but game isn't getting this info in real time: back when the artists were drawing the assets they used these photos as reference to draw their stuff, that's all.
Other games, they get in real time the day hour and the weather where you are located in the same way your phone get it from your weather app. This weather app, like any website is stored in a cloud. So the games have programmed different weater options and lighting depending on the hour, and instead of deciding using the game code the local weather and daytime they get it from this app (stuff like '18:23 - cloudy') and then the game renders the stuff locally as if this hour and weather would have been decided by the game.
Some flight simulator games instead of using their own air traffic programmed by their own, they get airplane locations of the real air traffic in real time from related apps or websites (so a cloud). So instead of setting these airplanes coordinates using the internal game logic, they get them from that app/website/cloud and then the game does everything locally like when these coordinates are set by the game.
This small info they get 'from the cloud' is pretty similar to when playing a multiplayer game and they receive stuff from other players: like info of where are they placed, in which direction are they looking at, what animation are they playing, if they have some recently shot flying bullet etc. They are only a few words and numbers, and then the games renders locally and applies the related IA locally.
These games (mostly driving or flying simulators) that use photogrametry or satellite data as reference to draw their game assets, or real time air traffic/road traffic to populate their 'levels', or real time weather or day time are normal PC and console games. They don't need to run on a cloud gaming service and don't need XCloud (it has the same feature set than their competition, some of who even performs better) or Azure (it has the same feature set than their competition, some of who even performs better) for nothing. If MS says other thing it's just PR bullshit like 'the power of the cloud' for Crackdown 3 and Mylo's miracle AI.