Yes, you're right: Chekhov wrote his play in four acts, not three. This Three Act Plot Analysis is just another way of breaking up the text to understand the way it works. With the meandering structure of Chekhov's plays, we need all the help we can get.
While there are a number of story lines in the play, the main story question is, "will the cherry orchard be saved?" So "Act I" in this case does seem to encompass Chekhov's Act I, when the orchard's nostalgic value is made clear and Lopakhin introduces the challenge of finding an alternative to the impending sale.
In "Act II," which includes Chekhov's Act II and most of Act III, we watch as Lubov and Gaev do absolutely nothing substantial toward achieving their goal (saving the orchard). Lopakhin keeps encouraging them to make a decision, but they refuse. At the end of this "Act," Lopakhin reveals that he's bought the orchard.
The family vacates the house, and Lopakhin starts building.