Hi Martin,

If you have DS80C390 manufactured by Dallas Semiconductor, then definitely it's ROMless. There is no doubt.
If /CE0 - /CE3 are called program chip enabled, this is because are outputs to CEs of external memory, in order to enable the external memory program. These pins can't be used like inputs, to program something inside controller. The words "program chip" are concerning to external chip (obvious with his own program).