5 days, not 6. He played the Sunday before the break and the Saturday after, then was given Sunday off. So he played 5 innings of fairly uneventful baseball (hitting into two groundouts and making one defensive play on a base hit to right field) sandwiched between 4 off days.
I think he played because he felt well enough to play, just like he played after the break up until he didn't feel well enough to play. It feels to me like it got worse in that 2nd Cubs game when he was removed from the game in the 8th inning.
I get Yelich's back issue is a big deal but pro athletes play through their aches and pains until it gets to a point where they just can't anymore. I think that has to apply to Yelich just like anyone else. He can have a sore back that he can play through, there's no known timeframe to take time off for rest so that it doesn't get worse, it could easily go as long as a typical trip to the IL anyway or longer. At least playing through it until he can't lets everyone know for sure that he has to shut it down so you're not playing the "what if" game. That's how I feel about it anyway. I'm sure there's room for disagreement there.