I've got a home gym in the back of my tandem garage. It's 11.5 x 11.5 with an 11.5 ceiling. Rather than working out in the box, we work out in the cube.
Here is a photo of the area:
A small space will require some smart design. You've got to protect floor space and wall space. Floor space for lifting, push-ups, double-unders, etc. and wall space for wall-balls, HSPU, wall climbs. In my space the wall space was not very useful where the window is and where a box protruded from the wall to house a water pipe shut off. So the window wall is where we store floor stuff (bumper plates, plyo boxes, etc.), and we put photos and keepsakes on the wall by the water pipe. We try to keep the back wall and the wall inside the rack clear.
I think your guess that 16x16 for two people to workout is appropriate. In my garage, we can have two doing deadlifts if one person is inside the rack. Two people can do cleans if the weights are light. Any snatches or max effort, and it's only enough space for one person.