Is it just me or is 'food' not implied by menu?

I had a look at the full OED. It tends to agree with you and suggests a menu is primarily a list of available dishes. Although it does qualify the other meanings we know about (i.e. in computer operating systems), and also suggests a menu is a list on contacts in a mobile telephone (I don't remember that usage).

Language does change, though, as as people have said, we're increasingly seeing menus split into types of food and/or drink.