Someone call it a Selection Indicator or Halo. I would like to know how to make this effect in BGE?
The best way to do this at the moment is having an object (the shape itself or a plane with a shape texture) that follows the Character, and turns visible or invisible depending on the character selection state. You should be able to do this even without coding, by using the visibility actuator logic brick.
Belated answer, but necessary. Parent.Blend This builds the ring at the current object, deleting it and reproducing it every .1 ticks.
It may actually be more efficient to parent it, which yes you can do in the bge, I just can't find the command that allows it. And another note, you shouldn't use real geometry for this effect(I only did because I wanted to build it quickly) you should use a plane with a circle image UV mapped onto it to reduce processing time.