Those bold underlined bits, that was 'The Point (tm)'. Or perhaps the controversy which ensued. However, bear with me just a little longer: I have not seen anyone saying "Romans are descendant of Armenians" or anthing so much as implying this. All we have seen is the (widely accepted) thesis that Latin is a derivative of a speculative Indo-European language of which its first natively speaker most likely hailed from what is known as Armenia. The Hittites are only one such people, but seems on a relative solid basis that they are the result of a migration from Armenia.
This says little about the Romans except their language is derived from an Armenian language; if someone therefore argues that the Romans were so influential by virtue of the widespread loan words from and existance of derivative languages today, he must a fortiori conclude that Armenians of long, long ago have been (especially in this regard) equally influential if not more (because this Indo-European language also similarly influenced Iranian and Germanic languages among others such as Sanskrit).
Ergo that argument merely serves to show the logical fallacy of the assumption that because of Latin's influence the importance of Romans can be shown. It cannot. For all that it matters, I think the Latin influences in our language are more a product of Medieval Latin, which was not even Roman Latin to begin with: Erasmus complained for some reason.
The only other argument I heard was that the Romans conquered such an vast amount of area. And spread its culture. Truth is likely closer to the idea that this culture spreading worked both ways, and at any rate much of the 'Imperial' (or indeed all) Roman culture was borrowed from other cultures to begin with. You may want to compare the effect of (ancient and continuous) policies of Chinese authorities to style the cultures of their realm towards Han precedent. Yet: it is Qin script and Chu food the Chinese are famous for.
Conquering a vast amount of area is a similar argument to that of the language thing. It is true the Romans conquered a vast amount of people, but it is dwarfed in the face of what some Chinese dynasties have conquered. Or compare the territory the Khans subjugated.
Bookmarks