Buying it in either the Windows store or the Windows Phone store results in the app becoming available on both platforms. The game's app listing has been updated to reflect this, and its price also dropped recently to $4.99.
This is the first universal Windows app. It's an area Microsoft is shockingly far behind on, considering Apple has featured universal iOS apps that work between iPhones, iPods and iPads for years, and even Sony has cross-buy games that work on PS3 and PS Vita.
However, Halo: Spartan Assault is also available on Xbox One and Xbox 360, and currently those versions must be purchased separately. (via Neowin)