Yup, it's because of the rotary engine in the RX-8. It uses oil injection at WOT high RPM for additional lubrication. This requires the oil to burn cleanly. What's interesting is that Mazda tested synthetic oils and some of them were OK and some were not. Rather than try to differentiate them, they simply said "no synthetics". Your 626 has a piston engine so synthetic should be just fine. In fact, a few of guys I know in SCCA ran synthetics in their rotaries with no problems either.