As far as I'm aware, if you're logged into steam on the second computer, it should recognise the fact you've already paid.
So I would try:
a) Install Steam on second computer
b) Log into Steam on second computer
c) Install Empire/Napoleon
hello, if I understand well ...
the steam keeps track of multiple users in separate folders and it gives the option to switch users. on my home, I have three users on the same computer with different games, but empire tw, for example, is installed separately on each machine(two)...
I'll try to understand how to create a new (me) Steam user on my other PC and install Empire under my user name and not my kid's (under which we installed Napoleon).