OMG! It's a MAGIC MONSTER!! Or as I like to call him, "Happy Fun Robot!" :D
I saw my first Magic Monster when I was 18. On my 28th birthday, a good friend of mine found a broken one, bought it for 50 cents, fixed it and gave it to me.

Mine came in the original box. It was made in Taiwan and has no branding or traceable info other than a Patent # 25814 and Lot # LS-020

You are the ONLY other person I know of who has one of these. You are indeed fortunate! Display your Magic Monster with pride as it "ya-yas" back and forth, spreading its message of mayhem!

BTW - The rubber faces ~are~ finger puppet heads and are available in weird little tourist-type toy shops. (They also graced the cover of an Anthrax album... See? I am a fountain of useless knowledge!) They were probably purchased in bulk by the makers of Magic Monster to use as the face.
I bought several replacements a few years back.