What is the url for the web version?

https://www.silvergames.com/fr/doodle-jump if you want ;)

I don't think this is the real doodle jump

Yeah this version isn't the real Doodle Jump, however, it is the version used for Web Speedruns. That is because it's faster than the version that is a direct port of the game, and it's been accepted in the community, so the only way to break a world record on the web version is to play on that weird version of Doodle Jump