This is a poor definition. It does not distinguish 'fascism' from previous authoritarian/nationalist movements.
Traditionally, one of the Right/Left differences, beginning at the end of the 18th Century, was nationalism vs internationalism. Another one was respect for traditional, hierarchical institutions -- 'Throne and Altar', plus the Army -- vs the desire to rearrange the political (and later, the social/economic) structure of society to be more egalitarian.
For roughly the first half of the 19th Century, the 'Left' was a 'bourgeois' Left -- the rising manufacturing/trading class counterposed to the old land-owning aristocracy. But as economic growth turned peasants into industrial workers, the 'Left' became a socialist Left ... and by the beginning of the 20th Century, was having a lot of success, in Europe at least.
The 'far Right' learned something from that success. And when the Bolsheviks overthrew the bourgeois-democratic Russian government and instituted the first socialist state, they learned something from that as well: the old model of a mass electoral party was outmoded, as well as the old Right program of veneration of the traditional social hierarchy.
The European 'far Right' became revolutionaries: they aped the Socialists' social program, and the Communists' organizational structure (a hard core 'combat party' of professional revolutionaries, rather than a mass-based electoral party).
Mussolini had been the editor of the Italian Socialist Party's newspaper. Hitler named his party the 'National Socialist German Workers Party'.
For political clarity, it's best to use the word 'fascism' for movements like this, not as a catch-all for any authoritarian nationalist movement. (After all, if authoritarian nationalist movements are 'fascist', then Fidel Castro and Mao Tse-Tung were fascists.)
Is there any possibility for a fascist movement, in this sense, in the US? Of course there is. The Republican Party has had a deep contradiction, for the last few decades, between its base -- increasingly, the bottom 2/3 of whites -- and its actual program and leadership, which has always been pro-business and upper-middle class.
Plus, the many of the ideologists of conservatism steal the clothes of the Libertarians when it comes to economics. They don't go quite so far as the genuine Libertarians and propose to auction off the National Parks, but they really don't like such welfare state measures as the US has, like Social Security and Workmen's Compensation and Medicare. But the Republican base would be horrified if their leaders actually moved to dismantle these programs.
So there is the objective possibility, as the Left's program to dissolve the foundations of America proceeds, for the growth of a hard-core, real authoritarian movement on the Right, blaming the usual ethnic scapegoats for our problems, evincing a leftish social program, and systematically forming quasi-military units.
A big military defeat abroad -- increasingly likely as our neo-con/neo-liberals try to maintain us as world hegemon -- combined with a big economic crash, might precipitate something like that.
In 1928, the Nazis got less than 3% of the popular vote in national elections. Five years later, they got 38%. Events can change mass consciousness quickly and dramatically.
At the moment, outright fascists are very unpopular on the Right, despite what liberals would like to , or pretend to, believe, just as outright communists are a tiny minority on the Left, despite what many conservatives seem to think. (For one thing, evangelical Christianity is still a major force on the Right, and most of these people are 'Christian Zionists', running straight into the anti-Semitism of the genuine fascists.)
But it could happen. (Also possible, but much less likely, would be the growth of a mass authoritarian/communist movement on the Left. By 'communist' I mean the real thing, not the pitiful scraggly anarchist mobs of spoiled brats we see now.)
So patriots must organize in anticipation of serious social disorder in our future, but at the same time be firm in our committment to the Rule of Law, with all the precious conquests of civilization that have gone along with it, such Free Speech, Equal Rights, the willingness to settle differences, where possible, through discussion and, if necessary, compromise. These are still valid principles even if our opponents on the Left are abandoning them.