I saw [this game][1] on Steam. They have a demonstration of the game in video form [here][2], and here's the GIF I generated from that video *(that's lower in quality and shortened due to the maximum 2 MB required to post)*: 

[![enter image description here][3]][3]

Basically, a cactus grows out of its post, and needs to push a plant into a hole *(or multiple plants into multiple holes)*. I want to know if this puzzle already exists with an official name, and if so, the exact rules to the puzzle.

For example, we know from the demonstration that pushing a wall would make the cactus grow, but what about pushing the plant into the wall when the plant is already against the wall? Would the cactus grow like that? 

And would the cactus be able to push one plant against the other, and continue to move forward by pushing one plant, as that plant pushes the other?

  [1]: https://store.steampowered.com/app/1471960/Room_to_Grow/
  [2]: https://cdn.akamai.steamstatic.com/steam/apps/256820935/movie480_vp9.webm?t=1612995755
  [3]: https://i.sstatic.net/co76Y.gif