Yes, some human sized animals can run for a few seconds over water - but not humans nor moose.

As other answers pointed out, the animal would need fins and a large power output - that is, large muscles arranged in a way that a large part of its power can be directed to efficiently move the fins.

Dolphins have both, and dolphin running over water (that is moving horizontally on water while keeping their body vertical and nearly all of it out of the water) is a trick usually seen in dolphin shows. It's often called "tail-walking".

[![Dolphin tailwalking][1]][1]

([image source][2])


It is even clearer in video. For example, see https://www.youtube.com/watch?v=A3tbypo870c

  [1]: https://i.sstatic.net/o388u.jpg
  [2]: http://www.sci-news.com/biology/tail-walking-dolphins-06366.html