Even if this paper is correct, the approach is not practical. From table 1 in section 6.2, the LP representation of a 25-city TSP requires 24,580,032 variables and 3,643,825 constraints. Merely formulating that model will require significantly more time than fully optimizing a TSP of that size using an assignment or 2-matching relaxation and adding subtour elimination constraints as they are violated. The former will likely take seconds (or maybe minutes) at that size, while the latter can be accomplished in milliseconds.