Depends on perspective.
On one hand, you have an agent playing in an environment with another agent also evolving. This falls under the definition of Multi-Agent Learning, as can be seen with works such as
Michael Bowling and Manuela Veloso. Multiagent learning using a variable learning
rate. Artificial Intelligence, 136(2):215 – 250, 2002.
However, I’m not sure which policy is saved
The policy from the Monte Carlo tree search is stored, as we can get the policy estimate from the network later by passing the given state through the network, which is used to calculate the cross entropy loss to update the network's policy (summed with Mean squared error loss between value head's prediction and ...