This is a video game about a six year old with a gun and I highly recommend watching this longplay video, probably the bit around 1:56
This was apparently originally supposed to be a Urusei Yatsura game but they appear to have not secured the license in time leading to this apparently hasty (and temporary, since by the time they released the NES version it was a Urusei Yatsura game) reskin. The music is from Urusei Yatsura, I assume illegally
According to Wikipedia, this was Japan's tenth most popular arcade game of the month of October 1986