The Quest of Ki is a linear game, although warps will allow you to skip ahead several floors at a time. On each floor, the goal is to locate and collect the key which opens the exit door, and then access that exit door before time runs out. Along the way, you may be able to collect treasure chests which contain items. Some of those items will help you, and some are even required to complete the floor. In other instances, the items in the chest may harm you (such as Poison.)
Starting on the first floor, you may find warps which transport you to another floor. The next floor that the warp transports you too will also contain a warp, up to floor 58. In this way, you can quickly advance through the tower, but the warp chests are typically more difficult to collect compared to chests containing other items. It is recommended that you only use the warps to return to the highest floor that you've previously visited in the normal fashion.
Your goal is to reach the top of the tower at floor 60. However, upon successfully completing the tower, you are given access to forty additional stages known as the "Special Stages." These stages are particularly harder than the original sixty, and contain guest appearances by characters from other popular Namco games.