Can I unlock any badges on the Stack Exchange network by playing Unikong?
Are there any badges on the Stack Exchange network that are unlocked by playing, or are otherwise related to, Unikong?
No, there are no badges you can unlock on any Stack Exchange site by playing Unikong.
This is similar to the last two April Fools games. StackEgg had no badges, and neither did the one two years ago, Unicoins.