ML licensing?

Hello!

I have a MacBook which I am quite satisfied with and which I use as my main machine. It runs Lion, 10.7.5, and everything is fine with it.

Now, for work reasons, I had to get myself a MacBook Air---which came pre-installed with Mountain Lion. It turns out, I need both Macs. And I know how it sounds, needing two laptops...but that's how it is, so bear with me.

THE QUESTION IS: Am I allowed to install Mountain Lion also on my other, older machine without having to buy it again?

I mean, they are both my own, personal machines---just like I don't have to pay twice to have an app on both (since they are linked to the same AppleID) I assume that if I had bought ML through the AppStore, I would somehow be able to download and install it also on the second machine.
The thing is, even if the new machine has been linked to that same AppleID, when I look up "OS X Mountain Lion" in the AppStore on the old machine, it tells me I have to pay for it.

Do I really have to spend money to get ML to install on my other machine?

If so, why does ML seem to be the only program I could find (up until now, at least) that forces you to do so?
If not, how exactly do I do that? Do I have to use some sort of workaround or is there an easy way I am simply not able to find?

Thanks for your help,
Nicola