It says that it looks like a string theory because string theory has an expansion in term of surfaces that has a similar power counting (replace $$N^2$$ with $$g_s$$). If you take the two index from the matrix like index in a gauge model, you can make the diagrams organize in a way similar to the large N expansion in gauge theories, like planar diagrams, genus-1 diagrams, etc., that has the same power counting-surface topology structure that string theory (there are people that says that eventually gauge theories will be strings because of this, I think they are seeing more than what there is). Also, some Matrix models end up reproducing type IIA and type IIB theories.
https://arxiv.org/pdf/hep-th/9610043.pdf
https://web.archive.org/web/20110605230843/http://igitur-archive.library.uu.nl/phys/2005-0622-152933/14055.pdf