The biggest problem is that it is ambiguous whether unlike describes "have ... the gift" or "does not appear to have ... the gift". Logically, this problem shouldn't be resolved by changing "unlike" to "like", but "like" binds more closely with "have" in this instance.
The deeper issue is that employing multiple negations that are only indirectly related is cognitively difficult, or at least not as easy as using at most one negation or using directly-related or completely unrelated negations.
- George went home. (No negations - easy.)
- George didn't go home. (One negation - still easy.)
- George didn't not go home. (Two directly-related negations - takes a moment, but not too hard.)
- George didn't go home without his hat. (Two unrelated negations, not too hard.)
- George didn't go home by not taking his bus. (Two indirectly-related negations. A bit of a head-scratcher.)
There's nothing wrong grammatically with the last example (or any of the above examples), but the indirectly-related negations introduce several grammatical possibilities that need to be considered.
Even the parsing is ambiguous:
- George didn't (go home by not taking his bus).
- George (didn't go home) by (not taking his but).
Then there's the question of how "by" interacts with "not taking his bus" - means? manner? purpose?
Your Russian masters example carries similar kinds of grammatical and semantic ambiguities.
Based on what I read of Fowler when doing some research for another question some time ago, I have the impression that clarity of speech was very important to him. As such, it would not be surprising for him to criticise such an awkward construction.
At @WS2’s suggestion, here’s an unambiguous, simplified version of the Russian masters example:
- Unlike his Russian masters, Mr Berger is in gifted at ....