Probably one of the starkest differences between wargames and any other kind of game I know of is the concept of the "critical hit."
For example, in the Down in Flames series of card games on aerial combat, an otherwise fairly "euro"-friendly light wargame, there's one Action Card that has an "Attack" result reading "Fuel Tank Hit, Aircraft Destroyed."
This, needless to say, an extreme result that can easily turn a game completely around, and it has little to do with a player's skill. Naturally, this sort of thing is an anathema to most game players interested in a contest of skill, even those otherwise comfortable with a certain mount of luck in their games.
Yet it's a pretty common feature of wargames, especially very tactical games, although it's not unheard of even in wargames dealing with higher-level operations.
Wargamers, as a rule, seem resigned to seeing an occasional game end with a spectacular bang, even though it might negate their winning strategy. While it might be rationalized as adding a little bit of excitement to a game, that really can't be the answer for why it's tolerated. After all, euro games like having excitement as well.
No, the answer simply is that real battles often turn on such fluke events. Every so often the HMS Hood has to blow up! Otherwise there's no chance for a historical result for the Battle of Denmark Straits.
Still, the existence of critical hits is a notable, if little-noted, difference between wargames and other games of skill.