Nobody cares about "interactivity" or "immersive" experiences except the devs who make them. People want to get their shit done as quickly as possible using software that feels simple and works as they expect the first time.
A SPA might be the best way to achieve that. But often it isn't.
That's not what the trend shows. Apps have added more interactivity like live chats, conferencing calls, more editing options (i.e. editing videos when uploading to YouTube), and this is probably going to keep going adding things like voice commands, customizable layouts, and more realtime information being displayed at any given time. The reason it converges with video games, is because both are clients and both process lots of user inputs and then display the result to the screen.
edit: i should add I'm not saying it's ALL going this direction, but certainly the big apps with lots of users.
There is jump going from "I see this happening" to "this is what user's want." For example, the trend is also towards massive tracking, more ads, and heavier and heavier pages. Users don't want these things, but business forces create them.
I think this is probably true of many (not all) of the kinds of things you are calling "interactivity". In any case, the reasoning isn't sound, even if you think your conclusion is.
Nobody cares about "interactivity" or "immersive" experiences except the devs who make them. People want to get their shit done as quickly as possible using software that feels simple and works as they expect the first time.
A SPA might be the best way to achieve that. But often it isn't.