I'd like to find out who Alice Moore is and if there is any family connection with Philip Moore, and maybe eventually find out if these Moores are in any way connected to the Collisters of Douglas/Santon, or the Clagues of Santon/Malew - in short to supply a reason for this document being found where it was.

I've found this burial of an Alice Moore at the right time:

MOORE, Alice Braddan/Onchan 27 Apr 1796 GELL

but I can't see a Will listed for her.

If that was the right Alice Moore it points to Alice Gell the wife of William Moore, and the following children:
Margt Moore d/o William Moore & Alice Gell 16 Dec 1743 St Matheus Chapel, Braddan [Familysearch]
Ellinr d/o Wm Moore & Alice Gell Nunnery Miln Oct 6th 1745 Braddan [Familysearch]
John s/o Wm Moore & Alice Gell Feb 29th 1749 (1750) Braddan [Familysearch]

but I can't see a marriage for Alice Gell (of Nunnery Miln?) and William Moore, or a clear baptism for Isable. I wonder if anyone has found them?

It looks like William survived Alice but there are too many William Moores to guess which one it might be.