Licensing can be a little bit confusing. You can definitely install on your second computer, even though it will take you a while to do the installation. That 2 week figure is for each individual license file. Here's how it works:
You ask JRiver for a license file. You then use this file to license one of your machines. Now that machine is permanently licensed. If you have other machines you want to license, you can use that same file, without asking JRiver for another one, within 14 days. After that, the file is no good. But any machine you licensed with that file is permanently licensed.
Weeks or months later, you can ask JRiver for another file and license more machines. Again, for up to 2 weeks with that particular file. You can make 10 of these requests per year, which normally covers most people's needs. In the rare event that it doesn't, JRiver is usually very nice about resetting this 10 count.
I hope that helps clear it up.
Brian.