Part of the search space though should also consider the global state of the game, which includes things like your own deck, which adds a further complication for forecasting branching.
And if you want to get truly smart, you also have to consider what the opponent might do, which, as viewed by the player, opens up the search space to a lot more cards both in their hand and in their deck.
So yes, each turn the branching options to play is relatively small compared to the other examples. However, the evaluation of future moves and the "true" board state is much, much harder and has a huge branching factor.
And if you want to get truly smart, you also have to consider what the opponent might do, which, as viewed by the player, opens up the search space to a lot more cards both in their hand and in their deck.
So yes, each turn the branching options to play is relatively small compared to the other examples. However, the evaluation of future moves and the "true" board state is much, much harder and has a huge branching factor.