You could export the animation either as a gif or as a spritesheet if your wanting to use just this animation you've set up.
However in a game engine you might be better off just importing each layer and writing some code to handle this.
Its a bit complicated but I know in Godot there is an option in the texture to have it repeat which could be used some how. I'm sure unity also has an option as well but I've not used unity yet.
Also, another idea I've seen before is a technique where you take the image and tween it to the left lets say and then spawn a copy all the way to the right off screen and keep that going which also moves to the left. Essentially while the one is moving off screen another is moving in to its place creating a loop effect.
I know there are probably atleast a couple handfuls of ways to do this though! :)