When you walk into an American store, and a clerk asks you "How are you?", do you really think he's interested in how you're doing? Dutch people generally hate that remark. It always makes me want to make up a story about how my dog was run over by a monster truck, and then to start sobbing in the middle of the store. That'll teach 'em to ask me how I'm doing, rather than if they can help me find the product I'm looking for!
"Good game" is the chess-equivalent of a clerk's "How are you?". If you can't come up with anything better, leave it out altogether.
I never say "Good game", so I can't (not) mean it.
I try to be more original than that. If I really thought it was a good game, then I'll mention the reason WHY I thought it was a good game. For example, "It was very close until the 34th move; do you remember the rationale behind move 35?" and start an actual conversation (if the opponent responds to my remark, that is). Or "Interesting game. I've never seen a position like the one during move 23 before..." "I really enjoyed our conversation during the game, you're very funny." "Boy, did you kick my butt! Once my ego has recovered, would you mind if I challenged you to a rematch?"
I hope you'll agree these remarks have some sincerity to them; in my opinion, if "Good game" is the best can come up with, then the game probably wasn't that good --a paradox if ever I've seen one.
On this site, some guy once said to me "Good game". I responded: "No it wasn't. You wiped me away." He then wrote: "OK, it wasn't. You suck."
I now consider him sort of a friend.