And he starts with incomplete data, as only 40% of the energy in coal is converted to electrical energy. Then, from that 40%, additional 5% are lost in transmission and distribution, so what reaches his flat is around 38% of that, or 2.6 kg of coal per kWh.
So one his coal powered lamp day is already, assuming his other factors are correct, around 5 kg of coal(!) or almost 2 tonnes of coal per year! Which is a huge footprint. Imagine that the same guy would have to just unload that much coal, delivered to his house, once a year, and to feed his lamp every day, would he still consider it "nothing"?
Burning hydrocarbons roughly produces 3 times more CO2 in mass, resulting in 15 kg of CO2 for one of his "lamp days". In volume, it's even more easy to see the size of that all: a kg of CO2 has volume of more than half of cubic meter (0.56 actually), so his lamp day produces more than 8 cubic meters of pure CO2 per day or 3000 cubic meters of pure CO2 per year. Enough to fill 25 European city flats with pure CO2 (otherwise, in atmosphere there's only 0.04% of CO2 -- that's 400 ppm talked about here: https://e360.yale.edu/features/how-the-world-passed-a-carbon... ).
"But the atmosphere is huge" -- yes it is, but still the change of CO2 concentration affects us. There is an experiment that demonstrates the effect with ink:
https://www.youtube.com/watch?v=81FHVrXgzuA
We don't see CO2 with our eyes, but the molecules of it efficiently block the parts of heat emissions (it is just electromagnetic radiation, just like visible light is) which would cool our part of the atmosphere. So the heat around us increases, just like it's warmer under a blanket (we are practically under always thicker blanket, and we add to it with our actions, just like adding the droplets of ink in that video). Everybody should understand that much.