Does a 2008 Miata have a timing belt that needs replacement or a chain which is good for life?

The latter...fortunately. The MRZ motor is indeed robust, and takes superchargers or turbos with ease. Assuming it's running well I'd be more concerned with rear unibody quarter panel rot or maybe a coolant leak. If you buy it absolutely chase fatter anti-swaybars and great rubber immediately. These will eliminate the poor OE body control. Both the 16" and 17" tire/wheel setups can handle superbly. Dumping the heavy OE muffler for a $150 straight pipe (Goodwin) while you're installing the rear bar is easy and worthwhile in grabbing 5+hp and dropping mass. The cheap OE front strut brace (OE GT) is useful for reducing cowl shake too. These mods total under $600 and will truly clean up and tighten the handling and body control in the twisties.

They have a timing belt with recommended replacement every 60,000 miles (100,000 miles if in California).

Sorry, Bob, but the t-belt ended with the NB series in 2005. The 2006-present use NC and ND use a metal CHAIN that's good for life. Otherwise I wouldn't have bolted on a Cosworth SC if I needed to disassemble for just a bloody rubber belt!

I stand corrected, I guess to be honest my only hands on experience is with the NA and NB models covering 1990 thru 2005. The Subaru Guru is correct, your 2008 has a timing chain not a belt.

How can a buyer of a 2006 MX5 be sure that it has a chain seeing that it’s manufacturing is very close to the change over period 2005/ 2006 ? Just asking

All NC VINs have chains.