Their map is claiming a lot of territory that never even nominally belonged to Mexico. By the 1819 treaty between the US and Spain, before Mexico won its independence, the line was drawn along what is now the eastern border of the Texas Panhandle north to the Arkansas River, up that river to its beginning, then straight north to the 42nd parallel and then along the 42nd parallel to the Pacific. So only the Oklahoma Panhandle and a small corner of Kansas were included in Mexico, along with southern and western Colorado (not including the Denver or Colorado Springs areas) and none of Idaho or Oregon. They did miss a small bit of southwestern Wyoming that nominally belonged to Mexico until 1848 (I doubt anyone ever saw a Mexican official there).