Andrew Garfield has clarified what this video was made for in a recent interview. Here's what he had to say.
"That was just me and Emma taking the piss. We were given these things to do for different stations and websites, and we said, "This one doesn't make sense." We can't say, "This is so amazing," so we sang it to make fun of it, and we didn't even think they would use it. We were so hyper and we had just gotten our second wind, so we were being just completely stupid and ridiculous."
The Amazing Spider-Man was released July 3rd, 2012 and stars Andrew Garfield, Emma Stone, Rhys Ifans, Denis Leary, Martin Sheen, Sally Field, Irrfan Khan, Campbell Scott. The film is directed by Marc Webb.