Calculating the computer's move may be a long running task, depending on the depth of the game tree (the computer player's level) and number of possible moves at each step. It's better not to run such a task on the UI thread, but use a web worker to run it on a separate thread.
Alternatively, Angular 2 allows running the whole app (well, most of it) in a web worker. Angular-CLI does not yet support generating new apps in this mode, nor setting this mode for existing apps. This post explains exactly how to do this. I tried it and it worked well in development, but then I ran into problems building the app for production, so I decided not to do this for now.
Before starting to handle this issue, it would be good to perform some measurements and see if there really is a noticeable performance issue. The maximum computer level is currently 5, and it may be that computers of our days can do this calculation fast enough.