I suspect it's a mistake. But if it is, the correct DC should be not 15, not 13, but 12. Yes! Twelve!
We know from the PHB that the DC for the Dragonborn's breath weapon is 8 plus the user's proficiency bonus, plus the user's Constitution modifier, making Constitution the breath weapon's "spellcasting ability." (Though it's plenty obvious, I should clarify that it's not a spell.)
The same calculation is used for the various dragons' breath weapons. You can infer a dragon's proficiency bonus by subtracting the damage bonus from the to-hit bonus of, say, its Bite attack. The Red Dragon Wyrmling's proficiency bonus is apparently +2; the DC for its breath weapon is 13; 13-8-2 = 3, and +3 is the Wyrmling's Constitution modifier.
This actually applies to the spell-like abilities (I use the phrase in a non-technical sense) of every creature found in the Monster Manual. If you do the math, the save DCs for the harpy's song, the cockatrice's bite, and the rust monster's antennae are all based on their respective Constitution modifiers.
Except for the breath weapon of the example Half-Red Dragon Veteran. Its proficiency bonus, based on its various weapon attacks, is clearly +2. Its CON mod is +2. The save DC for its breath weapon should be 8+2+2 = 12.
But the book says it's 15, and that doesn't really make sense. It may have been assigned arbitrarily to best fit the intended Challenge Rating of 5, but this would be odd, considering how consistently the Constitution-based calculation is applied elsewhere. It may have been calculated based on a much higher Constitution score or proficiency bonus, and then got overlooked in a revision when the Half-Dragon got powered down. It may have been a simple typo.
For all I know, the example Half-Dragon was extensively playtested with the printed numbers, and the number 15 was arrived at after months of careful balancing. But if we play by the (inferred, but consistent) rules of the Monster Manual, the breath weapon's save DC should be 12.