I sympathise somewhat with the claim. Fascism has evolved since political parties literally used it in their names and marched around in customised military uniforms.
There are certain narratives continue to demarcate modern fascism from other extremist politics. A striking one is the focus on a pure nation or race, and the idea that some impure foreign invader is conspiratorially undermining that nation, and dragging it down from its purity and former glory.
For Braun this is the gays and the Jews (as it was for Hitler); for Trump it's the Mexicans; for Farage it's the Romanians; for Orban the "non-Europeans"; for Bolsonaro the indigenous Native Americans, etc...
This is pretty distinct from, say, authoritarian communist narratives, which are often about liberating the workers of the world from their capitalist masters.