This is not a martini. This is chilled vodka served up with a twist. You can enjoy chilled vodka served up with a twist! That’s fine! You should drink whatever you want! But a martini is a cocktail.
Now, you can argue perhaps that martini has become a way of drinking, as seen in something like an ‘espresso martini’ which contains no vermouth but is served in a martini glass. Language does change. But that example is still a cocktail, not just chilled espresso served up. There are ingredients.* Call it whatever you want in your own house (and playing around with barware on your own time is so fun, please do it.) However...
When things like this become popular I wait for them to trickle down and someone to order one from me. Usually I don’t care - I loved when sbagliatos had their day for example, that’s a glorious drink (and a nice upcharge 😎). But if you come to me in my dive bar arcade, fail to read the room, and order a ‘naked vodka martini’ as I am seeing this called you are going to be in for a shock, because I don’t have martini glasses. I don’t even have glass glasses! You are getting a chilled (and therefore diluted) double shot of Titos in a Pizza Hut cup, my friend, and you are paying 16 dollars for it. Enjoy.
*(The lemon doesn’t count, and she swipes the pith not the peel, terrible form.)