My typical response is this...
As long as you *own* both computers, there is no requirement that you must purchase a unique license for each computer. I realize much (most) software specifies that you need a unique license for each copy of the software you install. Some are more lenient, allowing you to install multiple copies so long as only one is in use at any given time.
The stipulation with regard to Tournament Director license keys is that you do not share your license key with other people. I would hope this one is obvious.
So, if you typically run your own tournament, but then go to someone else's tournament and register their copy of the TD with your license key, this would be a violation of the license agreement. They should have their own license key.
But, for example, if you host tournaments at your own home using your desktop PC, and also host some tournaments at your neighborhood clubhouse using your laptop; or, if you typically configure your tournaments on your home desktop PC and then run tournaments using your laptop, you can certainly use your single license key on both of these copies of the software.
I hope that what you take from this assessment is this: I put a lot of work into the software (and continue to do so), so of course I want you to purchase it, and be fair about it. But I'm also trying to be fair, by supporting the software as best I can, by continuing to improve the software, and by not trying to wring every last bit of money out of each user that I can.