Even though "alt-right" is less precisely defined, it is in many cases more accurate a term than "facist" or "far right".
To me, alt-right is a combination of anti-establishment Republicans, fascists, libertarians, internet trolls (& governmental operatives trying to influence foreign elections).
To me the grassroots part of alt-right is more a reaction than ideology; something born out of the financial crisis and its' aftermath.
If you want to view them purely as fascists, that's your prerogative, but using THAT word would be less accurate and would lose a lot of nuance.