A DC motor is rotating a load with a constant speed. The motor has a potential difference of 12 V across its terminals and the average current passing through its windings is 1.3 A. If the total resistance of the windings is 1.7 Ω, what is the electric energy consumed by the motor per second?

Electrical power (in watts, or joules/second) for a DC circuit is equal to voltage times current in amps. However, the current flow in a DC circuit is equal to the voltage divided by resistance, and using your numbers that would mean that i = 12/1.7 = 7.1 A, not 1.3A as you wrote. So it seems that the data you have is inconsistent. If you use other forms of power calculations, such as P = i^2 R or P=v^2/R you will get different results because of this inconsistency.

I also thought it fishy but it is a question of district physics Olympiad... are you sure that it doesn't mean something else?

I can only assume that there is an additional resistance in the circuit inside the motor other than the windings. So I would ignore the resistance number, and use power = voltage times current.