Today I planned to buy the game for a friend, but when I got home to buy it, there was literally 1 minute and 30 seconds of time to buy it. Anyway, I think it was quite hilarious, but is there a record what was the time of the last purchase of the game? I want to know if someone beat me.

It's... not a contest. What do you mean 'if someone beat you'?

As it is, I think the only way you'll be able to find out when the last purchase was is by contacting the Humble Indie Bundle directly.