The total number of matches played is 14 + 13 + 12 +...+1 = 105 matches. Two points are awarded for each match, so in the tournament the total number of points awarded is 2*105 = 210 points. If the last place team got 7 points, and no two teams got the same number of points, then the point totals for each team from lowest to highest must be:
7, 8, 9, 10, ..., 20, 21
This is the only set of results that works out properly. Since the wining team got 21 points, and the only way to get an odd number of points is to have an odd number of ties. So the winning team must have had at least 1 tie.