I'm very particular about what I'll call a martini, but I recognize that it's pedantry at this point. To me, a martini needs both gin and vermouth (and I like mine with a splash of angostura bitters). Without vermouth, it's just a shot of gin. Without gin, it's just--something else.
You can't change every single ingredient and still call it the same thing, no matter what kind of glass you serve it in. If I take a hamburger, and replace the bun with a tortilla and the ground beef with refried beans, and the ketchup with salsa, I have a burrito. It's not a burger, even if you serve it with fries.