Well, to follow this "digression"
into European history, one of the reasons that Caesar was justifiably stabbed was for adding to the overall confusion of definition, by naming the people East of the Rhine "Germanic" (n.B. NOT "Germans"), so as to distinguish them from the "Gallic" (Gauls) West of the river.
Ever since then precision of defining has lost itself in translation into the various European languages.
Those that actually come closest to the Germanic self definition of "Deutsch" that today's people of "Deutschland" apply, being the equally "Germanic" Scandinavians with their descriptive prefix of Tysk".
The "Latins" of today hopelessly stick to totally imprecise definitions, Spanish and French actually clinging to the mistake of "Aleman" which, while describing a Germanic tribe, is about as relevant as describing the English as Saxons.
Italians, while still making the mistake of speaking of "Germania", being at least an exception in that they refer refer to "Deutsche" as "Tedesco", the next nearest thing.
"Germanic" dominance of Western and Central Europe may be ascribed, at least initially, to the rise of the Frankish empire (certainly Germanic), but seeing how two nations of today claim its most renowned leader Carolus Magnus for themselves (the French as Charlemagne and the Germans as Karl der Grosse), this makes the whole thing no less idiotic. He was as little French as he was German, seeing how neither identity even existed then.
The dominant "Deutschland" that is being referred to even today indeed did not come into being until various Germanic people were united (more by force than actual enthusiasm) under Prussian auspices in the 1870s. Even where the bric-a-brac collection of irrelevant German speaking piss-pot principalities that preceded "Deutschland" sired a greater desire among its subject for a "Deutschland", practically none of those wanted the upstart "Prussians" to form it, let alone lead it.
In conclusion of all of which the claim of "Germany" having dominated Europe ever since Rome packed its bags and left, is indeed historically as false as can be.