To better pin down the location, I georeferenced the map getting good match of all land and sea features with a reference map. The figure below shows it overlaid over a reference map with seafloor releif:
And the location of your mystery Island is were the red dot is, plus a 25 km search radius.
And the coordinates are (Lat/Lon): 17.0619° N, 152.177° E.
It nicely coincides with a seamount, so it might be more than an error on the map (but that seamount acoording to the data in Google Earth is more than a kilometer under the surface). What definitely seem to be an error, is including such island as part of the Northern Mariana Islands, because in all the references and maps I saw, that denomination only covers the 15 islands on the chain to the west.
I did a search for something in that location first looking as MODIS images (250 m resolution) on WorldView I had to browse trough months of images to get cloud free images, but I couldn't identify any island
Therefore, if there, it must be tiny.
After looking at the catalogs for higher resolution images, there are no Landsat images there at all (something that suggest there is no land there) but there are two Sentinel-2 scenes (10 m per pixel), and happily the cloud cover is not too bad.
I did a search in those two images within the 25 km radius displayed above.
This is the first image
And this is the second
And again I didn't found anything.
Therefore I'm inclined to think that there is nothing. But I can't rule out that something very small can be hidden by the clouds. However, I doubt it.
If you want to perform the search yourself over a larger search radius, just let me know and I can give you the images.
I also searched the seamount catalog for those coordinates and the only one that show up is Vlinder Guyot about 224 km to the East. So there is no information on the one below your mystery island.
However, in this publication. It is refereed as "I'l Ichev" and is part of the "Magellan Seamounts".
I also looked over the seamount you suggested ("Pegas" in the above map and located at 16.136° N, 151.968° E approximately), that is about 100 km away from the location pointed on the map you posted, but I didn't found any island there either (on a search box 22x26 km):
After browsing many other maps, I've also failed to find other map showing that Island. However, in a relatively similar location some old maps show "Los Jardines" Island. It is a know "phantom" island, some more info on its wikipedia page. Here a 1932 German map showing it:
Despite it is not in the same location, it might be the source of the confusion.
Here a list of good quality maps that DO NOT show that island: