Hm....the way my AM install works it is.
If I'm looking at a system display showing a wheel for all the games, when I press my Edit Game button, it brings up the "Edit Game" menu for the game I currently have selected in the wheel. In there I can choose which emulator, rename the game, etc. These edits are saved in the corresponding romlist text file.
If I'm looking at the main menu, pressing my Edit Game button brings up the "Display Edit" menu where I could choose what layout to use, which romlist, etc for the currently selected wheel item. These edits are saved in the attract.cfg file.
Edit: just checked, and this behavior is the same in Attract Mode as well as Attract Mode Plus