One game per reward. You just need to play 10 games over the next 4 weeks, with a limit of 1 reward per day that's passed during the first 10 days.

Shrengar

So it doesn't have to be 10 days in a row?

For the first 10 days every day a new reward becomes available. You can then play a game to claim a reward any time during the 4 weeks.

KasumiGotoTriss

If you don't play for the next 10 days, can you just play 10 games one after another in one day when you come back? Or will you still have to wait 24 hours between each one.

Yeah, you could burn through them all in one day once they're all released.