If the table is 72x72, that makes it 6ftx6ft. Ideally you want a rug big enough that when you pull out the chairs from under the table, you would want them to still be on the rug. Have you considered maybe a rectangular shaped rug? maybe an 8x11 or 9x12.

The space is square and the table is square. A rectangle rug is not an option. Sounds like you are saying bigger is better so 9'x9' is the route I should take?

Yes, you are going to want something that is big enough so when you pull the chairs out, they are still on the rug.

Figure at least 30" to pull out a chair. 3 feet would be better. That means adding 5 or 6 feet to the size of the table, At a minimum, you'd need a 10x10 rug, and 12 x 12 would be better. Those are odd sizes., but you can get a rug remnant bound to that size.

In a perfect world you'd have 36-42" all around the table for circulation, and a minimum of 24" of that space would be for the rug, 30"+ is even better. The chairs need scoot and sit room, and space behind so other diners can exit the table without requiring someone to stand and push their chair in for someone to pass behind them.