How do I calculate the landing weight in this situation?
First calculate your weight on the ramp:

$$
\mathrm{Empty~Weight} + \mathrm{Crew} + \mathrm{Fuel} = \mathrm{Ramp~Weight}\\
538\, \mathrm{kg} + 150\, \mathrm{kg} + 93\, \mathrm{L} \cdot \Bigg[\frac{0.72\, \mathrm{kg}}{\mathrm{L}}\Bigg] = 754.96\, \mathrm{kg}
$$

During Taxi, you said 2 gallons of fuel will be used:
$$
\mathrm{Ramp~Weight} - \mathrm{Taxi~Fuel} = \mathrm{Takeoff~Weight}\\
754.96\, \mathrm{kg} - 2\, \mathrm{gal} \cdot \Bigg[\frac{2.72\, \mathrm{kg}}{\mathrm{gal}}\Bigg] = 749.52\, \mathrm{kg}
$$

Then subtract the weight of the fuel that will be used on the trip:
$$
\mathrm{Takeoff~Weight} - \mathrm{Trip~Fuel} = \mathrm{Landing~Weight}\\
749.52\, \mathrm{kg} - 10\, \mathrm{gal} \cdot \Bigg[\frac{2.72\, \mathrm{kg}}{\mathrm{gal}}\Bigg]= 722.32\, \mathrm{kg}$$

(Source of conversions)