A couple of things going on here: Idiom error and adjectival clause issues.

First off, it should be 'fascination with.' Get rid of (C). Next, notice the comma splice in (A). Also you do not want 'this' floating around without modifying a noun. For this reason you can also get rid of (D). (E) is a relative clause that requires a verb. That is, 'whose inauguration...' should be followed by a verb somewhere in the clause. So eliminate (E).

That leaves us with (B), that correctly uses the participial phrase 'marking the inauguration...' to serve as an adjectival clause modifying the main clause.

(A) Jurassic Park, this was the inauguration of both a new style of film-making and the audience's fascination with dinosaurs
(B) Jurassic Park, thus marking the inauguration of both a new style of film-making and the audience's fascination with dinosaurs ANSWER
(C) Jurassic Park, both inaugurated a new style of film-making and the audience's fascination from dinosaurs
(D) Jurassic Park, and this was the inauguration of both a new style of film-making and of the audience's fascination with dinosaurs
(E) Jurassic Park, whose inauguration [No Verb] of both a new style of film-making and the audience's fascination with dinosaurs

(B) it is.

@ Chris : Verbs are needed in relative clauses always ?