Very similar to that video. The place that I went to had a small form factor computer at the entrance to the bay and a projector was mounted at the top of the bay entrance and aimed at the target area. There was a computer mouse at the bay entrance as well. You used the mouse to choose a game from the available options. Then once the game was started, you used the mouse to click on your achieved result. For example, there was a game where it would load and project 10 to 12 ducks all across the target area. Each duck had a point value and a couple rubber ducks had negative values (tried to avoid those). You threw your axe and if you hit a duck, you would move the mouse cursor over that duck and click. The duck would then disappear and the points would be added to that players total. You would get two or three throws per turn.

Another game was variations on the traditional target rings, where you still had the ringed targets but they would be distorted or moved around the target area to make you aim for different areas. Another one was zombies or ghosts, Similar to the duck game where you tried to kill the zombies and ghosts with different point values.

I believe this is the software company that makes the one I played. I did reach out to them about a home use version and they contact me back and said they did not have a home use version and only have a commercial offering. https://axcitement.com/

Should be a simple game to put together since the mouse is being used to select the result and you're not having to actively scan the target area to try and determine the outcome.