Unfortunately not quite the right manual, but it certainly gives a decent idea of what's happening.
Presumably the resistor is R22 from the circuit, coupling from opto-triac to main triac. It's shown as 50 ohms, but has 47 ohms in the pictures in the manual, either would be fine, it's not critical, and 47 is a standard value.
However, the degree of burn-up is quite severe, so perhaps the main triac has failed?, or the opto-triac?, or both?.
I think I'd simply change all three.
The second resistor (not shown on the circuit) looks to be OK, and is just marked by the damage next to it.