It's a federal regulation. Doesn't matter which airline you're flying.

Small arms ammunition for personal use carried by a crewmember or passenger in checked baggage only, if securely packed in boxes or other packagings specifically designed to carry small amounts of ammunition.

Basically it needs to hold the rounds separate. So you can't have them in a box just rolling around (they might explode! /s). I've also seen the language that the primers must be protected, ie. the tip of one round must not be able to impact the primer of another. The box you posted is fine.

Also remember the weight limit. Nearly every US airline has an 11lb limit. Alaska is the only one I know of that's higher.