Of all the characters Google could have picked for its offline game, why a dinosaur? The answer is a small, clever joke.
The prehistoric pun
Being stuck without an internet connection is, tongue-in-cheek, like being thrown back to the "prehistoric ages." So the Chrome team chose a prehistoric creature — a Tyrannosaurus rex — as the mascot of the disconnected web. The gag writes itself: no internet, welcome to the age of dinosaurs.
Why a T-Rex specifically
The T-Rex is the most recognizable dinosaur in pop culture, instantly readable even as a tiny pixel sprite. Its short arms even became a running joke in the game's design.
More origin details are in our dino game history, and you can meet the T-Rex yourself on the home page.