The author concludes that an effective acting performance does NOT call attention to the fact that it’s a performance.

Why?

Because if it did call attention to the fact that it’s a performance, that makes it more difficult for the audience to empathize with the actor’s character.

And, effective acting performances do NOT detract from the audience’s appreciation of a play.

One premise gives us this relationship:

Effective acting performance → NOT detract from audience appreciation

The other premise, if we think about it in terms of its contrapositive, gives us this relationship:

NOT more difficult for audience to empathize → NOT call attention to fact of performance

We want to get from “effective acting performance” to “NOT call attention to fact of performance.” To do that, we want to establish a connection between the two premises:

NOT detract from audience appreciation → NOT more difficult for audience to empathize

Here’s the contrapositive version of the relationship we want to establish:

More difficult for audience to empathize → detract from audience appreciation