If you own a house without a mortgage, then that reduces your living expenses, which means that you need a smaller stash than you would if you had to pay rent or a mortgage in retirement. So the house you own counts that way.
If you are downsizing after retirement to a place on which you will have no rent or mortgage and are freeing up cash at the same time, then there may be smaller living expenses that your stash has to cover (tax, bills, repairs) plus there is extra cash for the stash.
So one way or the other, the value of your house does count in the stash. The thing to avoid doing is counting it twice, or counting the value that you are currently living in which is over its "spare cash if we downsized" value.