I think the term YouTuber is mostly use by younger internet users. I guest YouTube members are called YouTubers because people think it sounds cooler, or people are too lazy to type YouTube Member.
But, I notice people rarely call members on other video sites Vimeoer, Dailymotioners, Bliper, or Metacafer, and they are typically called members, content creators, and video creators.
I think it is a matter of Youtube being more popular and also the fact that Youtube has been used as both a noun and a verb.
For instance, to Google something, means to use or search Google.
A Googler, is one who Googles.
It is the same as a baker being a one who bakes, or a racer, being one who races. etc.
Youtube, in essence, would be no different in this regard.
I've heard people use "Youtube" and "Youtubing" as both a noun and a verb on many occasions and so, using the word "Youtuber" is a natural progression from that.
It is the popularity of the place that I think the term was invented from. I would not say it was because they were younger or anything like that. Just something that caught on because of it's popularity.