RAW, the Engine should be affected...
...but that doesn't make much sense.
I am currently running this adventure for a table, and while I believe you are correct that RAW, the Engine should technically shut itself down, I also believe that that doesn't make a lot of sense given the greater context. My chief support for this can be found in the description of the Engine itself (p. 188, emphasis mine):
... once activated, it does strange and unpredictable things on each of its turns until it is deactivated or destroyed.
The implication here, I believe, is that it keeps going. Note that none of the other effects listed in the table mention the engine shutting down. Further, you brought up that the effect has a duration. I believe the presence of a duration in the effect is additional evidence that the effect is supposed to last until changing to something else, and that can't happen if the engine shuts off. I do, however, admit that designer oversights like this have indeed occurred before, and aren't outside the realm of possibility here as well.
Let us also extend your quote from the previous page:
The engine shuts down if any part of it comes into contact with an antimagic field or if it is targeted by a successful dispel magic (DC 19). Otherwise, it can only be shut down by a wish spell or divine intervention.
This tells me that the engine should be difficult to deactivate, given both the spells required and the DC, and the engine shutting itself off randomly seems to undermine that.
While I again agree that the engine should technically shut itself off, and it is always up to each DM to rule what they believe to be correct for their table, it is this DMs interpretation that the Engine should continue wreaking havoc until either the adventurers shut it down themselves, or
the 13 rounds complete and the engine sinks.
When my party finally reaches this I do not intend to run it in such a way that it could shut itself off randomly.
We can also refer to this answer on how the Maze Engine encounter functions for additional possible evidence that the Engine should continue running until
it sinks or is shut down by an outside factor.