As a swift action, you can expend one use of mythic power to cast any one arcane spell without expending a prepared spell or spell slot. The spell must be on one of your arcane class spell lists and must be of a level that you can cast with that arcane spellcasting class.
You don’t need to have the spell prepared, nor does it need to be on your list of spells known. When casting a spell in this way, you treat your caster level as 2 levels higher for the purpose of any effect dependent on level. You can apply any metamagic feats you know to this spell, but its total adjusted level can’t be greater than that of the highest-level arcane spell you can cast from that spellcasting class.
A player I'm with in a campaign is using this to cast spells as a swift action. I had this ability in a previous game, and used the swift action to empower my next spell cast that round. I by no means think the player is powergaming, as it's honestly an unfortunately-vague description. Which of our interpretations describes the correct usage?
As I read it, you cast any spell from your list, as a swift action.
No other action is mentioned. It doesn't say to use a swift action and apply it to the next spell you cast. It says you expend a use of mythic power to cast one arcane spell, as a swift action.
It costs a swift action to activate, but the action economy still requires the standard action to cast the chosen spell. Wild Arcana is limited to spells with a standard action or less casting time.
This was a commonly misunderstood rule in the early days of Mythic Adventures and one that continues to get misused unfortunately.