Is it safe to build a drop down table to a wooden wall?
Ideally you would follow the manufacturer's directions for mounting the drop down table to the wall. Also consider that the flat rail that is against the wall just under the table top area would be best if it could be screwed into the studs in the wall and not just through some thin wall board material. 

This table at 79cm wide should be wide enough that the support board can span at least two studs in the wall. You may need to adjust the mount location in order to achieve that.