Respectfully, my mom was in labor at this precise time.

So you were born!  Now I kind of get the question.  I'm guessing I was eating lunch at uni.

In terms of games.  Prime was probably my focus or another run of RE Remake.

I was in first grade at school. I don't think I was sick that day or at a doctor's appointment.
Had only seen a few video games at that point in my life and hadn't played any. But Christmas 2003 that changed with GameCube and GBA.

I'm not sure about that specific date and time but I was 5 years old and I got a GBA SP that year which I got a lot of use out of. I remember going to my mum to read some text for me cause my reading capability wasn't good enough yet for a game with a lot of text.

Took the weak to play Remedy games and Watch Anime.

Early 2003 I was 9, during January I was on school vacation, so naturally I was playing the best game ever, The Legend of Dragoon, on my PS1.

I was probably finishing up playing something for the day, or at least playing something if not finishing up yet. Most likely it was a PS2 game, but it could've been some PC game as well. I have no idea what it could've been though, because Metal Gear Solid 2 is the only game I could more or less time from roughly that time period, and it was released almost a year earlier, so the chances are that I was mostly finished playing it.

Probably being told to pay close attention by my first-grade teacher.
Boy, she sure was pretty.
I was probably distracted thinking about how I was going to beat Misty in Pokemon Stadium.

Playing the hell out of a modded PSone, when I could finally afford games for it. It was Resident Evil 3 most likely with some Crash Bandicoot 3 sprinkled in. I was also doing this on a tiny 7 inch, portable, black and white TV :D It sounds horrible, but those are some of my fondest memories from my life.

We talking about 2003!?
Well, likely playing Ragnarok, Diablo II LoD, Counter Strike, Warcraft 3, ZNES/GBA roms or on some POKEMON tournament (likely at SMOGON)