I'm having the same issue as of today, when playing my purchased copy of Mass Effect Andromeda using the EA desktop app. I don't have an active EA Play subscription.
It must be a bug, but I suspect it could be related to one of two things. Either the EA desktop app is mistaking our fully purchased games for EA Play games with daily limits (as others have speculated), or it's due to one of the EA app's settings being bugged out. In Settings > My Playtime there's a Playtime controls setting that lets the user set daily and weekly playtime limits for themselves. Mine are both set to "unlimited", but perhaps it's sending notifications anyway.
Update: I stopped the pop-ups from appearing when I disabled playtime tracking. In the EA app > Settings > My Playtime, scroll down to Playtime Controls and click Manage. Scroll down to Playtime Tracking and click Disable.
I also tested by leaving it enabled and set to the lowest time (30 mins), and sure enough I got the warning at 30 minutes instead of 10 hours. Setting it to 12 hours or Unlimited, it still pops up after 10 hours. Anyway, it's obviously a bug with the app's Playtime Tracker rather than some limitation related to EA Play.
