Here is an overview of each game, via Sega:
About Space Harrier
In this third-person rail shooter with pseudo-3D graphics, you, as the young warrior Space Harrier, must save the peaceful Land of the Dragons from vicious creatures. With the help of the dragons and your superhuman abilities, it is up to you to blast your way through a variety of treacherous landscapes in order to defeat these beasts and save the day!
About Puyo Puyo
Based on the original arcade release, you’ll need to keep your reflexes razor sharp in this simple but highly engaging action puzzle game. Your objective is to create combos with four or more “Puyos” of the same color, all the while preventing these colorful blobs from reaching the top of your playfield. It’s a battle of skill and endurance in this entertaining game filled with charming characters!
Read more about Sega Ages Space Harrier here.