I hear red orbs summoning in a different dimension and I think Bakugan. It's another spin on the pokemon/digimon/beyblade/yu-gi-oh/... idea of having a game be the one thing that governs people's lives, including bad guys also using it to try to take over the world.
In this one, players have both little balls and cards. Fights begin by both players flipping over a card dramatically, which transports them and any plot related allies to a pocket-dimension. A turn (sometimes) consists of throwing down one of your cards to (sometimes) join up with cards already in play. These cards form the battlefield for your 'Bakugan', which are small orbs, which you have to throw on top of the battlefield. In some episodes it's important which card they land on, in others it doesn't matter at all. These orbs then transform into large monsters, which (sometimes) fight the opponent's monsters in the same square, (sometimes) receiving bonuses from the cards the fight takes place on.
The abundance of sometimes in the previous paragraph is explained by the larger than usual inconsistency in the rules for fights throughout each episode of the anime.