What do the British mean by "bolshie"?
Over 50 years ago I was perfectly familiar with the "playground slang" term bolshie meaning uncooperative, recalcitrant, truculent (Oxford Dictionary of Modern Slang, 2010). That was long before I knew anything about the political etymology - which later knowledge hasn't significantly affected how I've used and understood the word over the decades.
There are probably still some Brits who see overtones of US commie in the term even today, but it's worth noting that there was no equivalent to McCarthyism in the UK, and the British public at large never really perceived any threat from "reds under the bed".
It may also be worth noting a couple of hundred written contexts where bolshie occurs in close proximity to stroppy (obstreperous = bad-tempered and argumentative), very few of which carry any political overtones. In fact, I'd say the adjectival usage ("Why are you being so bolshie?") is effectively "orthogonal" (Def:3) to the much rarer noun usage ("They're just a bunch of bolshies") that etymological dictionaries are always so keen to tell us about.
In OP's specific context I don't think there's any "political" connotation to the usage. The reviewer just means...
although superficially the prose appears to reflect nothing more than mindless hostility/negativity (towards everything), closer examination reveals evidence of a finely nuanced writing style.
Definitions from online dictionaries:
a bolshy person often argues and makes difficulties: He's a bit bolshy these days. - [Cambridge]
difficult to manage; rebellious - [TFD]
difficult or rebellious - [Wiktionary]
stubborn, argumentative - [Urbandictionary]
deliberately creating problems and not willing to be helpful - [MacMillan]
As in my comment we tend to use it colloquially when someone is being unnecessarily aggressive, argumentative or generally 'anti-' about something.
Although I am more inclined to agree with your original line of thought and substitute bolshie for radical; radical can be defined as thorough, complete, total, comprehensive, exhaustive, sweeping, far-reaching, wide-ranging, extensive v nuanced: subtle difference or distinction in expression, meaning, response. Which actually contrasts rather well.
Bolshie is a shorten version of Bolshevism which was a radical socialist movement formed in Russia early in the 20th century. Bolshevism and its forms has been used by numerous right-wing newspapers & politicians as an accusation against their left-wing counterparts more radical elements. So much so that colloquially it has almost become a byword for radical.
Bolshie is short Bolshevik which means socialist. It has come to mean contrarian, uncooperative, or inclined to protest; probably stemming from derisive descriptions of left wing movements that lash out against the status quo.
I think the real key meaning is "dogmatic" or perhaps "fundamentalist" which is the "perceived" position of Bolsheviks within the socialist movements of the early 20th Century -- as opposed to the Mensheviks and/or Social Democrats, for example. Whether or not it was fair to describe Bolsheviks as dogmatic, that is perhaps how the term in the UK came to mean hard-line, aggressive, etc. Obviously, dogmatic in politics could be taken as an antonym for nuanced. Bear in mind, of course, that socialism's right-wing opponents often could not (or would not) distinguish the various strands within the left, and would call even the most faintly progressive person a "bolshie." In North America, at least since WWII, the term Commie would be the derisive diminutive that would stand in for the UK-English Bolshie. In fact, over here, I've never heard Bolshie used in the more general sense of aggressive or hard-line.