Correct, PT8211 is a different protocol. It is quite similar, but key details differ, so PT8211 does not work with I2S.
The i2s_quad output has been tested with two SGTL5000. It should also work with pairs of other I2S chips, though PJRC only tests SGTL5000. But two PT8211 chips will not work with quad I2S.
Some of the NXP/Freescale documentation calls the on-chip peripheral SAI (Synchronous Audio Interface) and sometimes they call it I2S. Really, SAI is technically a better name, since it is very flexible. It can be configured for TDM, the special format PT8211 uses, and lots of other ways. I2S is only the most commonly used protocol.
I believe it should be technically possible, given enough time and programming skill, to create a quad PT8211 object. I have not tried this, and as far as I know nobody else has done it.