According to evolutionary theory, dinosaurs lived tens of millions of years ago, while giant sloths lived merely millions of years ago. So the writer is speaking whimsically of the history of the Internet, placing it on an evolutionary timescale. He's trying to say that he got involved a long time ago, but not at the very beginning. That is, long enough ago that he was before the giant sloths, but not so long ago that he was in the time of dinosaurs.
It's sort of kind of an idiom to use dinosaurs as a symbol or metaphor for something that is very old and out of date. People will fairly often say things like, "Wow, your cell phone is a dinosaur", meaning that your cell phone is very old and obsolete. Not specifically cell phones, but anything that could be old and obsolete, from electronic devices to business practices to political or social ideas.
It's not common to use giant sloths in such an analogy, but in this case the writer needed something else to put on the time scale.