The answer you linked shows that this formulation is non-convex.
As for the claim in the paper you linked https://arxiv.org/pdf/0810.2311.pdf that the Non-Negative Matrix Factorization (NNMF) is actually convex, that's only true under a non-standard definition of convex optimization problem.
Specifically, in section 2.2.4 of the paper
This can be cast as convex multi-objective problem on the second order
Unfortunately multi-objective optimization problems, even when they are convex, they have local minima that are not global
Per p. 6-17 of the lecture notes https://class.ece.uw.edu/578/fazel/lectures/problems3.pdf
convex vector (multi-objective) optimization problem
minimize (w.r.t. cone (partial order) K) $f_0(x)$
subject to $f_i(x) \le 0$, i= 1, . . . , m
$f_1, . . . ,f_m$ convex
But a K-convex function is not a convex function. Local minimum is not a global minimum.