I'm not sure what this game is called, it's in Japanese so if somebody can translate the title, please let me know :blah:
http://www1.axfc.net/uploader/S/so/S_64403.rar
Type 'kai' in the first box without the quotes and in the second box, enter the captcha to download the game. It's still unfinished and the game is big because it contains the resources for the next levels. I'm pretty sure it only has the first level.
http://en.wikipedia.org/wiki/The_Quest_of_Ki
If i gather it right from the translation, it's a remake from that game. Though in the original, Ki was able to fly, not just double jump.
Just to warn you this game can be incredibly frustrating gameplay wise and the people on the board I found this game on were complaining it runs very poorly.
To double jump, hold up while jumping again. Right shift is dash. Press F4 to play the game in a window. Once in windowed mode you can change the keys. You have several attacks but you don't seem to need them at all to beat the first level.