Do right-wingers actually think Hitler and the Nazis were socialists because “socialist” is in the name?

Probably.

The thing here is that socialism is an ideal far from practice for any large group, merely a seasoning in the spice rack of governance. As far as that is concerned you're not going to find a uniform socialist group. Any percentage or criteria that isn't full blooded embodiment would be arbitrary. Who's a socialist, the 75% alignment? The one who is more socialist than anything else? The Nazis did use socialism. It's not in question, you just decide where the line is. I'd be hesitant to consider it a superior position unless you do only accept the fullblood to be a socialist, otherwise you're both on shaky ground. Even that's a little hard to claim due to the marxists and the original socialists being in conflict.

Antifa is what they say, not purely though. The rest of the conclusion does not follow because they are in opposition with pacifists for example and, while they may call them fascist sympathizers or some such, I doubt even they would or could stretch an identity of fascist out of a flowerchild.