Allthough it is an idle game it is still PVP. The team you create gets put up against a team of the other players. So technicaly still PVP.
But the maingame will be more of an active game like the trading card games in real life. Turn based and stuff like that. For that the effect texts on the cards will be coming into play.
yes you are completely right technically even now it is a PvP
What I wanted to express in the comment was that active human intervention in battles is minimal because:
That is exactly why I got interested in your game, I think the idea behind the game has a lot of potential and I am sure I will have a lot of fun playing it when it is complete ;)