The save points are the desks with phones. There are several per level. In the video, the first save point is at 1:20. YOLO difficulty has no checkpoints, but that's disabled from the start. Kid's mode will restore full health from checkpoints. I could put in a checkpoint after the starting sequence to get players ready for what checkpoints look like.
Edit: For the next update. I've added the first checkpoint to show up after the tutorial stuff.