You are right, it is a global coordination problem. There are two moves: Cooperate (i.e. reduce your CO2 emissions) or Defect (burn baby, burn).

Obviously there are many global actors but we can model it simply as a two-player game: Europe and the-Rest-of-the-World.

Its economic payoff matrix looks something like (oversimplified and with direction only; scale appropriately):

  v Europe/RoW -->    Cooperate     Defect  
  |-----------------------------------------|
  |    Cooperate   |    (0,0)    |  (-1,0)  |
  |----------------+-------------+----------|
  |      Defect    |    (0,-1)   |  (-1,-1) |
  |-----------------------------------------|

If Europe cooperates and the RoW defects, Europe loses relative economic advantage and our world still burns.

If Europe defects and RoW cooperates, Europe gains relative economic advantage and our world (maybe) still burns.

If Europe defects and RoW defects, nobody gains an economic advantage and our world burns to a RCP8.5 crisp.

Obviously the preferred siutation is everybody cooperating so our world doesn't burn and nobody gains or loses an economic advantage. But the Schelling point is everybody defecting and burning our world to a crisp.

Everyone ought to push for global cooperation; we've all gotta live here and it'd be nice not to burn our only planet. But if Europe cooperates while the rest of the world defects (i.e. the current situation today), you're an idiot.