It has been a few years since I played the game, but I roughly remember the basics and can fill in the holes from re-reading the rules.
At its heart, Dinomite is a typical children's track game where the first one to reach the end wins. The dinosaur theme is rampant. The six playing peices are different colored rubber dinosaur models of different species (some more famous than others).
One unique feature is that there is no straight path but loops around with about 10 intersections. Some of the intersections are called "Dino-Stops" If you end a move (1d6) on a Dino-Stop, you immediately roll again and move in the direction matching the number you rolled (e.g. 3 up; 2 left; 1,4,5,6 down).
Thus you can find yourself taking a longer path or even turned around and backtracking. The board has some other special spaces that require special rolls to cross a lake or get out of a mud pit.
The other major gameplay component are the dino-egg-venture cards. You optionally draw a card when you land on an egg-venture space. The cards are pretty varied, e.g. Move X spaces in any direction, Go to X, Take another Turn, Turn around and move X spaces, etc.
The varied cards and the looping nature of the boards make the play time pretty varied. The gameplay is very limited with few minor decisions, but it is good filler for any young child, especially one into dinosaurs.