I consider any serious attempt to play a design, given up due to frustration, as having "played" the design in question.
I agree with this. I have lost track of the number of designs I have started but didn't complete because they were broken, unbalanced or outright terrible (especially designs that give you no clue what you're supposed to be doing and expect you to touch every square in the game just to trigger an event that might progress the storyline one inch along the path). I've always considered those as "played," whether finished or not.
Oddly, the bad designs receive less reviews than the good ones. I think people would rather gush over a great design they've played rather than badmouth someone for putting together something terrible. Most of us just move on to the next design or thing we're doing and try to wipe it from our memory.