Shocked some more(!) I am that someone might make a derivative work to rebut ideas in it.
If it actually treated with the ideas in LotR, I might be sympathetic. But it doesn't actually. It attributes ideas to the LotR that are not found in it, and which are often as not contrary to the text itself. It's an ugly fabrication.
And if a writer of some foreign nation created an original epic based on the mythos of that nation, I'd probably be very sympathetic to it. It wouldn't disturb me in the slightest that a Russian equated Westerners with dangerous invaders. Heck, as blatant of a propaganda piece as the Stalinist work 'Alexander Nevsky' is, it's still a great work of art, and Tolkien's work is far more nuanced than 'Alexander Nevsky'. And among other things, Tolkien's work - to the limited extent it addresses colonialist themes at all, and for the most part it doesn't because it's grounded in medieval mythos and not colonialist or post-colonialist - it's explicitly anti-colonialist.
As a test, here is how you know you've hit the mark when bringing a different perspective to an idea. If the person with a different perspective is required to defend as reasonable your take on things then it's truly a different perspective. If for example Tolkien upon reading 'The Last Ringbearer' would have been inclined to argue that even with the different perspective the elves are still the good guys, then you know you've done well. But neither I nor Tolkien need to defend the 'people of the West' as imagined in 'The Last Ringbearer'.
Besides which, I'm wondering if you've actually read it. On the whole, 'The Last Ringbearer' does not really take umbrage at the whole east/west colonialist thing. In fact, this shouldn't even be particularly surprising considering the guy is Russian, and if we wanted to have a talk about colonialism and the eradication of native peoples and cultures folks from Russia would not have a moral leg to stand on with respect to lecturing anyone. I strongly suggest anyone investigate Russia's history of treatment of the aboriginal peoples of Asia if you want to have a discussion about colonialism. Eskov certainly isn't interested in that discussion.
No, the real thing that burns the britches of Eskov is Tolkien's Catholicism, theism, and as he would have it anti-intellectualism, anti-rationalism, and Luddite tendency to reject technological progress. The fight in 'The Last Ringbearer' is between Reason (as symbolized by the Orcs) and Magic (as symbolized by the Elves). This is not a simplistic East versus West conflict in Eskov's version of the history either, at least if you mean by East and West the real world's east and west. According to Eskov, 'The Lord of the Rings' is about the rejection of reason, and not especially about "Colonialism" or even "Racism" except to the extent that the forces of Superstition use that to advance their cause. The book ends with magic/superstition defeated, and the survivors of the war entering into an new age of Enlightened Industrialism.