Sort of. Sometimes it's deliberate, but they're really just another terminal state (different win/loss conditions, like you get 10 points for getting either character to their room, but 30 for both). Often, though, it's because puzzles and such aren't well considered so players are able to do things that prevent any further progress (unintentionally). This means the game won't terminate (or will take unreasonably long, like sitting for 40 turns for a timer to finish counting down).

In the example (simple) game in the post, a player character may be able to pass into the red room and "win", but perhaps there's no condition for returning and the game only terminates when both make it to their individual rooms. If the other character lacks the keys to move through the green and blue doors, then they will be stuck and the game won't terminate. This is easy to guard against in a small game (small state space, easy to manually or mentally compute), but in larger games it's almost trivially easy to cause these sorts of dead-end states. Consider the puzzles of Sokoban, where pushing a block onto certain walls or a corner prevent further progress and require a restart. Now, that's part of the game in that case, but perhaps a designer wants to prevent (in their puzzles) this sort of situation from occurring. This sort of analysis of the game model (states and actions) will help them prevent it.