To actually answer the question in a thread that I've already posted in, a game should be considered unplayable when due to framerate issues, glitches, or unreliable player controls, a game cannot be completed with regular consistency by someone who knows what they're doing.
For example, the 360 retail version of The Wolf Among Us has such a poor framerate, and such awful skipping that I believe it would be impossible to constantly perform the required QTE sections successfully. Beyond that, it stutters so badly that it seriously harms the storytelling and the overall experience. It's a broken and unplayable game.
Games with game-ending glitches should also be referred to as unplayable, and not just concerning the main quest. After putting in over 200 hours into Skyrim, I ran into a glitch that made me unable to complete the warring factions quest. This was my last major quest string available. I went back to the game over a year later and found that the problem still hadn't been patched.
I enjoyed Skyrim quite a lot, but for me, it became unplayable at this point. If your game has game-ending glitches, I feel people are justified in calling your game unplayable, at least when it comes to their personal experience.
Lastly, if a game's controls are so unreliable that no one can have a consistent experience when playing, I feel that should also be referred to as unplayable.
That's about it, really.
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