Does the "Go outside" achievement keep track of time across machines?

I'm currently in the process of unlocking the "Go outside" achievement in The Stanley Parable (in other words, I haven't touched the game in quite a while). I'm aware there are ways to unlock this achievement by changing the system time settings, but I'd rather unlock it the legitimate way.

However, I'm about to get a new computer and I'm not sure if I'll be able to keep my "progress". Normally I'd assume the game stores a timestamp of my last play session in a cloud save, but since the system time appears to be involved, I'm not so sure. I'm afraid that if I launch the game on my new machine, it will think I've never played it before, even if five years have passed in reality.

Do I have to start the game on the same computer after five years to get the achievement, or will Steam keep track of the timespan for me?

As far as I know from here (it talks about SquareLogic, but it should applies to all games), Steam check your SteamID to calculate achievements. So, if you change your computer but you're going to use the same account name, you should get the achievement.