No, Steam is agnostic to ecosystems beyond some rules.
Just like MS and XBL in Steam games, Sony will do the same with PSN likely integrated directly in the games. We might not see it off the bat, but that is where they'll go. Games are already a huge revenue stream from the unique users there. Then they can extend features that add value to games in that ecosystem for recurring revenue (switch between cloud and local play via PSNow sub, curated games via sub etc etc).
Steam has taken a vendor agnostic approach to these ecosystems for years. MS have been doing it with their games and XBL. Terms seem good enough that you have folks like EA jumping back on board, bringing Origin Access across as well soon. Seems Valve are doing the same with Cloud gaming solutions alongside their own.
Ultimately, these vendors recognise the unique audiences services like Steam have on PC, particularly a large amount of people never moving from the platform, but who have interest in PS games. So Sony, like MS and others, meet the gamers where they are to get friction-less access and expand their own ecosystem. Cuts become trivial vs the benefits.
Ecosystems is exactly what this is about. They don't care where you play, they just care that you play the games, and hopefully use their services. Same on consoles to come. MS don't care if you don't buy the consoles. If you are a PS die hard and get xCloud for a few exclusives - they are happy with that, they got you into the ecosystem