The game should save the co-ords of the ship and block's collected, would be a pretty small log to keep and only keeping the last run. Then you could reply the run allowing you to record it, or the game to render the frames and dump to disk.
Many games do this these days, TF2 and SpaceChem to name two.
Raw uncompressed would be nice for those of us who like to edit the video, and ofc an option to compress (.ogm or webm as they are free) for those who don't want to edit and just straight upload.