While you have two fine answers already, it is important to note that Persky warns Kugelmass against using the machine again. The underlying note is be happy with what you have...in the present. However, Kugelmass insists, and while the machine is working, Persky has a heart attack, the machine bursts into flames, and instead of the novel Kugelmass expects to end up in, he finds himself in the middle of a Remedial Spanish textbook. Not only is the "large, hairy" irregular verb tener (to have) chasing Kugelmass, it is "over a barren, rocky terrain" that this occurs. This description of setting again supports the idea that it's not getting what you want in life that is happiness, it's wanting what you have.
The irony of being pursued by the verb "tener" is a reminder of how elusive our wants and desires can be. Perhaps it is telling us that people don't want what they have, and they can't have what they want. The ending is significant in that it suggests that the destructive cycle of desire and deceit must be broken. If we spend our whole lives looking for eternal happiness, we will only end up with eternal dissatisfaction.
It is ironic in the end that Kugelmass, who has been in pursuit of things he thinks he must possess, is then pursued in the end by a large, hairy thing that wants to "have" him. (they both were in pursuit)
I somewhat disagree with the other respons.
As Allen has taken us through this odd tale, he has done us all the kind favor of tying up all his loose ends. For example, Emma "spoke in the same fine English translation as the paperback." or Sidney's (and Persky's) ignorance of the effect their meddling has on the text of the tale.
I think that Allen was simply trying to end this story; perhaps he thought it had gone on long enough. He certainly did not ignore the hilarity of the situation. Perhaps he wanted to leave us with the mental picture of Kugelmass running...forever running from the unavoidable price of his lust...for a monkey.
CD Sutton II