Projector mount with 2 or 3 screws
There are a few ways to play this


Mount a 2x4 on the other side of the ceiling (attaching the 2x4 to the joists with screws) and mount the projector to that. Unsightly, but it will definitely hold without any questions. Painting the 2x4 would help make it less noticeable.
Screw another 2x4 or 2x6 (can't tell from your pics) into place for the second side of the mount. Drill some small pilot holes in the ceiling to tell where it needs to go.
Mount only 2 screws into a stud. Use toggle bolts for the drywall side. It should hold well enough.
Use 4 toggle bolts. 8kg is about 20lbs, and that's well within the tolerances of toggle bolts. This carries the most questions, since the drywall has to hold all the weight. It should, but it may not since it's clustered so tight around the mount. If they used 3/4" drywall it should be fine.