Then compare Game Pass to PS now where Game Pass has more subs and I guess you can compare PS+ to XBL Gold. Gold also gives you games so I guess with your definition it's a game sub service too? The streaming point is moot because with both PS now and Game Pass you can download games to play locally on your system. Well I guess you can stream PS3 games on PS4 and play 360 LOCALLY on Xbox so I'd still say the MS service is better.
PS+, PS Now, Gold, Gamepass (both normal and Ultimate), Amazon Prime, Apple Arcade, Google Play Pass, EA Play and more are all subscriptions that give you downloadable console games. So all these ones are (downloadable) game subscription services, so I think they can be compared even if they may include other extras.
PS Now, Game Pass Ultimate (not the normal Game Pass), Amazon Luna, Stadia, Nvidia GeForce Now and maybe other ones I may forget are subscriptions that allow you to stream games, so they are game streaming subscription services, so I think they can be compared even if they may include other extras.
PS Now and Game Pass Ultimate are both (downloadable) game subscription and game streaming subscriptions, so I think they can be compared if you are comparing services that include both downloadable and streameable games, even if they may include other extras. But Game Pass Ultimate, not Game Pass. Because if you get the normal Gamepass for Xbox or PC you don't have game streaming, you only get the game downloading part. So this is why I include the normal Game pass in that group of services that have downloadable games but not streamable games.
Amazon Prime is NOT a competitor to Game Pass or PS now so I don't what point you are trying to make. Prime has movies and free shipping for Amazon stuff and neither Game Pass nor PS Now do that so I guess Amazon wins with your thought process?
GamePass, PS Now and Amazon Prime are subscription services that offer downloadable games, so they are competing. I had Amazon Prime mostly for the movies and series, but they started to include PC games so I got many of them from there. I got 3 months of Game Pass PC because I got subscribed to Discord, so now I'm playing PC games from here instead of games I got from the Amazon Prime or free in the Epic store.
It isn't my thought process: out of all the downloadable game subscription services, PS+ is the biggest one for console, Amazon Prime is the biggest one for PC and Apple Arcade is the biggest one for mobile. Out of the three, Amazon Prime is the one with the biggest amount of subscribers and revenue generated.
Regarding game streaming platforms, according to the numbers we have PS Now is the biggest one available for console and PC. And regarding consoles the only available as of today. Both xCloud for consoles and PS Now for mobile are still on the works, they announced to be working on it.