The claw machine was a nice way to break the ice in the atmosphere, some would say. And the reason was, once you were indulged and engrossed with how to get the stuffed animal in the claw, you'd forget everything else.
You could start talking to your worst enemy standing next to you, and even if you had been nervous, it would immediately disappear.
The game was an icebreaker.
So, Yun-tae saw this as a good opportunity.
"Sure." He answered. If Kang-woo and Chin-hwa were having problems with their friendship, then the best way would be to get their heads clear while they spent time together.
Since Chin-hwa was the one who brought up the idea, Yun-tae felt his motives wouldn't be suspicious, unaware that Chin-hwa also wanted to use this opportunity to get him closer to Kang-woo.
(I guess eventually we're running around in circles, not a triangle, haha)