I've found Metasequoia seems to be able to export obj files that import properly into ASP. Downside is that the developer is Japanese so finding tutorials could be a challenge. Also, obj export is only available in the paid version, currently $45.
Note: Besides the mtl file, be sure to include the texture file (jpg, etc.) in the same folder.
Regarding that video, my guess is that those figures were exported from Poser as bitmaps with alpha, not as 3D obj.