What is the following wireframe, mesh topography style called and how can this effect be applied to a figure in a photograph as done in the image?
This is not something that would be called a "wireframe mesh" in computer graphics. Models are sometimes displayed as a wireframe to help visualize the topology which look like a lot of connected lines but are nothing like the given example.
At best it could be called a "surface" if it was described using curves like the Utah Teapot but then I would expect it to look something like this:
If only the curves in a particular direction were kept, considerable more curves added in the chosen direction, thickened and stylized with noise then it would start to look something like what you are talking about. (visibility occlusion would have to be dealt with somewhere along the line)
To go from a photo to a stylized surface like this would involve converting the objects in the photo to models using something like photogrammetry. (which typically involve dozens to hundreds of photo's) Then figuring out a direction for the curves then creating control points for all the curves from the model, remove all curves that don't follow the chosen direction, and stylize the lines with noise and signed distance fields, then add in some more noise to the curves control points, and extra control points to help stylize them. With hand tweaking to get the final desired effect.
The entire process would be pretty involved. This could be a fun masters project (or maybe a dissertation if you could get it approved).
The really fun part if you got far enough along to have the code that does all this, would be animating the entire works. But I get a 5 aspirin headache just thinking about the work involved here.
Or just open some modeling software like Blender and create a texture that wraps a 3d model, or better yet, get the out the electronic art pen and touch screen which brings me full circle back to art/design suggested by Nathan Reed.