West Point Fort is about 40 miles up the Hudson.
If this fell into the British hands, then they would control most of the Hudson Valley and split New England off from the rest of the Country.
As New England was the centre of the Revolt, British control of NE would take a lot of the steam out of the Revolution.
I question that at this time the strategic damage would be all that great. This was after Burgoynes failure; there was no large army to take advantage around there.