Hey! Yeah, Blender refuses to acknowledge gif format exists :D
Here's the steps for rendering an animation:
-Provide either frame-based or video input;
-Check the "cyclic" and "auto refresh" options;
-Edit the "end time" value in the timeline to match the number of frames of your input;
-Modify the render output settings as needed (set output path, format, resolution etc)
-Render -> Render animation (default shortcut Ctrl + F12)
Hope this helps!