The game in question is Guandan, where you and your teammate try to make poker hands to discard your cards before the opposing pair does, which lets you level up. Teams can only win the entire match by reaching level A while avoiding having the player who discards all cards last.
The game looks interesting, has anyone played?
While I have not played Guandan specifically, it is a climbing game, like Big Two or Tichu, which I have. The main difference seems to be scoring by the card rank level and the wild cards.
BGG entry: https://boardgamegeek.com/boardgame/273913/guan-dan
My partner loves card games, I’ll have to give this a shot!