I think you need to make an important distinction here-- when people purchase your game, they own that specific "copy", but you retain the underlying rights (your copyrights, trademarks, etc.). So even if they own that copy, the thing you're selling is the physical or digital copy and not your underlying rights. In order to use that copy, the purchaser needs a license to those rights. If you're planning on transferring aaaaaall of those rights, you can only do it once-- once those rights are assigned, they can't be taken back except in specific circumstances (you'll learn about those if you read into recent comic book law). So even if you say "I want to sell the game, not license", it doesn't make sense unless you're planning on assigning your rights to a single purchaser.
I guess I find this a little confusing. Do movies, music, etc. have EULA's? Music is copyrighted, and if I buy a copy of it I own that copy, but not the rights for the song itself. This is accomplished without any EULA, so what is the difference between that and software? Or am I missing something?
By the way, I have contacted a lawyer, and I am going to get a EULA written up, but I'd still like to understand this stuff better. For one thing, I know what I want, but I don't seem to be able to express it very well.