JRiver licensing is done in a very different way than most programs. It's REALLY generously licensed though. They allow you to license all of the computers that you personally use/own (within reason).
Whenever you want to license a computer for JRiver, you need a license file. That's what should have been mailed to you. Those files end in .MJR. Since you have a master license, you can use that file on any version of Media Center. Were you able to license your Mac version of MC? If not, get that MJR file to your Mac and run it with Package Installer. That should license you.
Now, what about this 14 day thing? That's confusing isn't it? The deal is, since JRiver allows you to license as many computers as you own, they let you use the same license file as many times as you want. Once the license is *installed*, it's permanent for that computer. BUT: The file you use to do this expires in 14 days. That way, you can easily license all the computers you have, giving you two weeks to do it. After that, the file is "dead" and not usable any more.
What if you need to license a computer outside of that time? Like when they release MC21? No problem. Just go to the restore page and ask for a restore. That will mail you a new file, that's also good for 14 days. Again, once activated, the licenses are good forever. It's just the activation file that expires. JRiver will allow you to ask for new files up to 10 times per year. They call this a "restore". I think the terminology is confusing. But the process isn't too bad once you get it figured out. Oh and if for some reason you use up your 10 restores, JRiver will normally reset these and let you have more. As long as you have a decent reason. They are trying to be extra generous about licensing, while at the same time protecting their intellectual property and preventing rogue users from abusing the system and licensing computers for their friends, or worse, for pay and profit.
I hope this helps clarify things for you.
Brian.