It's collective, coordinated, and directs attention toward an individual on stage, as opposed to an individual expression of support like clapping or cheering - which many people might do simultaneously but isn't normally coordinated outside of a music performance. The 'as one' hand slamming you mentioned emphasizes the coordination here; it's novel, but basically an iteration on the original gesture.
> The complaint is that the twitter poster decided to sensationalize that rally by calling something it's not.
The tweet is somewhat hyperbolic and sensationalized, but while it's not exactly the same I really think it's more similar than different - it's a choreographed gesture of support for a political figure at a political rally involving a straight arm salute. As I said earlier, harping on the cosmetic differences sidesteps the very obvious question of 'does this look like a nazi rally to a casual observer?' And that matters, because political rallies aren't intellectually rigorous exercises in philosophical inquiry, they are theatrical performances designed to motivate political behavior through emotional arousal.
> That's all well and good if you want to demonize those groups, but what do you call people who actually want to systematically murder jews?
Groypers (this is an in-joke). We also have open neo-nazis who are explicitly aligned with the historical national socialist movement to the point of fetishizing it. The broader right wing authoritarianism that obtains in multiple countries at present can be generally described as fascism without any loss of precision or clarity. This doesn't have to refer to the-Italian-party-once-headed-by-Benito-Mussolini. Obsessing over typologies is sometimes a coping mechanism to avoid engaging with an issue, like having an argument about meteorology to avoid admitting you should have brought an umbrella.