It's not a chain that gets dirty like a bicycle, doesn't travel very fast even if attempting to row fast so doesn't need anti-fling properties.
I'd say just give it a wipe over then use a bit of the Woolies oil. If you wipe the chain with a bit of clean tissue and there's still a clean oily residue I'd not even bother re-oiling it. The "service schedule" is there to cover all questions I shouldn't wonder and to cover manufacturer. No gym will ever give their rower any form of service or maintenance.