I will venture a guess and it's only a guess. I was in LGA last week and there is a lot of construction going on. The NOTAM talks about a crane a 406ft. crane to be exact, if I am reading that correctly and the Lat/ Long puts it at the center of the terminal.
I do know that the MD-80 gets freaky on approach if there are obstacles not in the certification plane of that LOC or G.S. The airplane will porpoise on short final if the ground plane for the G.S. is uneven or if an auto-land is attempted on a runway not normally approved for that type of landing. The MD-80 autopilot is first generation and uses radio altitude rate information in the fare mode which starts just after passing 200'agl. Runway centerline tracking via the localizer and wind correction is also applied when flare mode is annunciated, it is a very flaky process on a CAT 1 runway, and even kind of weird on a fully Cat III runway.
This tower is 406 ft, and MDA for all Categories are 305 and 5000RVR. That puts the tower above published minimums.
As I said at the start, and it's just a guess, this NOTAM may be to protect the Localizer and Glideslope reception field which might be very disruptive to an autopilot, due to a large crane / tower.