Home equity payments are savings in the same way that any debt repayment is: instead of spending the money on consumer goods, you're using it to increase your net worth by reducing the value of the liabilities on your balance sheet.
That said, I don't count home equity as part of my "stash." Even when you pay off your home completely, it's not an income-producing asset. At best, I consider it part of my "margin of safety," as I live in a high-cost area. If we retire and economic conditions cause the 4% rule to fail for us, selling the house and moving to a cheaper area is one of many possible ways to make up the difference.