Three BASIC ways to renew a CFI certificate:
1)Taking a practical test for CFI.
2)Complete an approved FIRC.
3)Present a satisfactory student pass rate to FSDO.
So no, the ATP checkride (or any checkride other than that for a CFI) would not count toward the CFI renewal.
There are four, so I corrected your statement......
1. Passing a practical test for ...
(or) Presenting to an authorized FAA Flight Standards Inspector:
2. A record of training students showing - least 80 percent of those students passed that test on the first attempt
3. A record ... showing... in a position involving the regular evaluation of pilots
4. A graduation certificate showing that
But the OP still doesn't know how to find the answer or is too lazy.