Yeah you got it. The non diode will work OK for now but I'd always recommend replacing like for like.
Strangely the new Triumph relay (smaller one) doesn't look like it has a diode...
The new Triumph relay (smaller, more rectangular one) is a micro relay, Triumph started using them in the Rockets in March 2013 AFAIK, but it's not a replacement for your original one. They should still supply the older relays for the older bikes.
04 to 13 bikes have relay sockets for the big square ones and 13 onward have the smaller sockets for micro relays.