The Gremlins costume is a Ben Cooper, but I have no idea why it says STAR. It should say STRIPE, the only Gremlin named in the movie. At the time, even though I adored Gremlins (kids were literally running out of the theater, scared shitless—it was awesome), I would have been all over that Dr. Doom costume. In ’83 and ’84 my pursuit of comics was approaching mania.
UPDATE (10/12/15): Thanks so much to Shawn Robare for pointing out that the Gremlins costume does indeed say Stripe. My reading of “Star” was an optical illusion.
Here’s the Ben Cooper Gizmo costume.
There was also a full body Gizmo costume. Here it is in action.
And here’s the McCall’s pattern, if you want to try and track it down. Notice the box with the painted air holes (not included).
(Photos via bobcat135/Flickr, Sean/Flickr, Needleloca, and Etsy)
2 Warps to Neptune 
It actually does say Stripe, it’s just misleading with the folds 🙂 http://www.retrocrush.com/archive2003/costumes/stripe.jpg
Ah ha! That drove me NUTS. Thank you!