The same article also says:
> Historian Ian Kershaw once wrote that "trying to define 'fascism' is like trying to nail jelly to the wall."[28] Each group described as "fascist" has at least some unique elements, and frequently definitions of "fascism" have been criticized as either too broad or too narrow. According to many scholars, fascists—especially when they're in power—have historically attacked communism, conservatism, and parliamentary liberalism, attracting support primarily from the far-right.[30]
So, rather than purporting to define "fascism", the article acknowledges it has many definitions and it is contested which one is right. Read in the context of the whole section "Definitions", I don't think the opening sentence should be read as a definition, except in a very vague ballpark sense, which isn't meant to be used in decisively answering the question of whether any particular thing is an instance of it.
Furthermore, it mentions key elements of historical fascism – anti-communism, anti-conservatism, and anti-liberalism – whose presence in Putin's Russia is debatable. Putin has criticised communism, but he tends to go for nuanced and qualified criticism rather than the demonisation of it which was historically found in Mussolini's Italy, Hitler's Germany or Franco's Spain. He isn't anti-conservative either. Nor is he rhetorically opposed to parliamentary liberalism – he is accused of undermining the substance of it, but he pays it lip service, unlike Mussolini and Hitler who demonised it.
The first actual definition it gives in the "Definition" section is this:
> Historian Stanley G. Payne's definition is frequently cited as standard by notable scholars,[31] such as Roger Griffin,[32] Randall Schweller,[33] Bo Rothstein,[34] Federico Finchelstein,[35] and Stephen D. Shenfield,[36] [37] His definition of fascism focuses on three concepts:
And the first of those three concepts is:
> "Fascist negations" – anti-liberalism, anti-communism, and anti-conservatism.
I say Putin lacks all three – he isn't anti-liberal (you can say he is in a contemporary sense, but not in the historical sense that Mussolini was, which is I believe the sense Payne means), he isn't anti-communist (again, not in the sense Mussolini/etc were), and he isn't anti-conservative.