Also, to me we're talking about two different kinds of luck when we talk about (a) a situation where the rules of the game intentionally put luck into the game via coin flips, dice rolls, e.g. and (b) luck via external things like "I might accidentally come across a great strategy" or "the grandmaster might be sleepy".
The rules of chess have no luck built into them. The rules of Dominion do. Both games can be affected by the external luck of the better player making a mistake or being drunk/sleepy, or the novice accidentally using a good strategy.
In addition, the chess example can be complicated by considering the following two situations:
1. Play a normal game of chess. At the end, flip a coin, if the coin comes up heads the person who won actually loses instead.
2. Play a normal game of chess. At the end, roll a 6 sided die. If the die comes up 1 or 2, the person who won actually loses instead.
These are different situations because in #1 it makes no difference whether you checkmate the other person or not because your chance of winning is 50% regardless. But in #2, checkmating gives you a 2/3 chance of winning vs. 1/3 for the person who got checkmated. So in #1, your chess strategy has no effect on the outcome but in #2 it does. I have no problem saying that #1 has less strategy than chess, while #2 has the same strategy (but with the strategy having less effect on the outcome than in normal chess).
EDIT: I should make it clear that I'm happy with the luck/strategy quotient of Dominion and I don't see the need for a house rule.
EDIT 2: You can add a third situation to come up with luck reducing strategy but not completely eliminating it: Play a normal game of chess, but if you try to take a piece with a Queen or Rook, you have to flip a coin, and if it comes up heads you have to skip your turn instead of taking the piece. There's still strategy in this game but it's not the same strategy as regular chess.