"Sport" is defined as athletic activity, and "athlete/athletic" refers to physical exercise, agility, stamina, and strength. So no, playing a video game doesn't count.
If girls make you sweat, good for you. Sex could arguably be athletic, depending on what you get up to.
I'm not the one who brought athletics into this. I'm just following the conversation. But no, "esports" do not meet the definition of "sport."