It's a 4x bonus (on "miles" earnings), but for this particular airline (SWA = Southwest Airlines), the normal earning is a flat 600 Southwest points per stay (rather than a small number of miles for each dollar spent, as it is with most other ailrines).

So it's not the bonus itself that's "stay" based, it's earning Southwest Airlines points that's "stay" based (and thus using Southwest Airlines in a miles promo is "stay" based, even though it's "spend" based for all other airlines in the same promo).