That being said, I'm still surprised Youmu lost, but it shows that much like the Touhou itself, there many more games to play in the future.
Youmu actually did win. Remember that each of the Four Senses have to be called "-sama" by everyone, and at the end, Yuyuko called Youmu "Youmu-sama".
I thought the last panel was supposed to represent Youmu being announced as the winner of the tournament, but this makes sense as well. The chapter seemed to imply Remillia won at first but the last panel confirms it indeed was the half-phantom! Also, it's hard to tell from the drawing but when Aya was looking at the photo with the winner, Youmu was in it but not Remilia. When it came to Patchouli talking about the final match, she most likely was talking about an alternative outcome rather than what had actually happened (I don't know anything about Mahjong but I don't see what else she could have been explaining).
Other than that, It's funny but not surprising that Youmu lost much of her motivation and dedication to the game after she achieved her goal of making Yuyuko proud of her.