I've seen Umberto Eco's checklist simultaneously be rejected and accepted by the left. Some will say that it's non-Marxist and prefer not to use it, but if anybody here says "the enemy is both strong and weak," nobody (that I've seen) rejects that rhetoric device.

Ur-fascism should be understood and used as what it is, an essay on the semiotics of fascism. It works as a critique of ideology, and it works very well in that regard. What it does not achieve at all, because that lies outside of the scope of that essay, is explaining the historic and material roots of fascism, which is where the usual Marxist explanations come into play, such as the essay you're quoting, or the definition by Dimitroff that expanded upon Stalin's theory of social fascism, Trotzkis counterpoints to that (that put more emphasis on the role of the petit bourgeoisie), the (debatable and in my opinion subcomplex) "agent theory" used in the DDR or later post-colonial variations like the concept of Foucault's Boomerang or Fanon's writings. When used correctly, Eco isn't contradictory to these, but complementary.