LÖVE

I want to create animation to use it in my videos. I don't want to create games. Does your engine support export to mp4 or avi format? I want to make animation and save it to video files. I personally love the animation of Fishy Bits 2 game.

Short answer: No.

Long answer: No, But you could make an animation, and save each frame of it to a file, then assemble the frames into a video with pretty much any video editing software.

To save the frames you could use love.graphics.captureScreenshot