Since it is supposed to be a race, I assume it is on a specific course layout. All these hypothetical speed calculations are fine but if we were to encounter the REALITY of an actual race on an actual course, we must take into account other factors.
Most importantly, one must take into account the animals intelligence and trainability (can you get them to follow the course, go on the start command, not be distracted by or eat the competitors etc).
So let's just take some of the animals mentioned:
Cheetah--Not very trainable animal. Hates water. No way in hell are you ever going to be able to train it to jump in the water, and swim in a straight line 100m to a designated end point. It's going to get in the water and turn around and scramble right back out at the starting line as fast as it can.
Otter- Very very smart animal. Very trainable (learns complex tricks, can do mazes etc). Would easily follow the course. As mentioned, pretty fast in water and on land.
Seal- reasonably smart. Very trainable. Not as fast on land.
Polar Bear- smart but pretty nasty and not as trainable as black bears but still probably doable. Might maul a couple trainers until he gets it right.
Moose-??? They are known for being stubborn. But, I have no idea overall if they are trainable.
Horse (not sure if this animal was mentioned and I'm too lazy to go check)- smart enough. Definitely trainable. Would definitely follow the course. reasonably decent swimmer, much faster than moose on land.
Hippo-- Who cares how fast it is. It is one of the nastiest, ornery animals around. Good luck getting it to follow the course or even start.
Human--intelligent (although still dumb enough to possibly wipe itself and the rest of the planet out but that's another story). Trainable. Would follow the entire course for sure (unless it's got Katie Holmes disease). Medium speed in water and land.
Based on using criteria necessary to complete an ACTUAL race, I would say the finish order after 3 months of training would be:
1) Otter
2) Horse
3) Seal
4) Human
5) Polar Bear (possible DQ though)
Cheetah--DNF Hippo--DNS
The moose could be a wild card...