I got two copies [wireless and wired]. I tried the wireless Dragon 10 CD [identical looking to the wired version on offer here] on a second desktop PC. It installed, loaded and registered OK and ran without comment [registered using the same details, e.g. me and my address and same activation code on CD]. The auto-updater has now run and downloaded the 161Mb service pack 1, but it only activated after a week or so delay [but that happened on my original install as well - but you can download and save this massive service pack 1 to the hard drive]. So YES I can install easily on a couple of PCs.
Why not buy one copy and try installing it on both anyway [you want to evaluate it first]. I was impressed how easy it was to dictate after the initial training was over, although I still get some words stuck like: 'X it' for exit, despite retraining the word. If you are happy to use the mouse for a few edits it's pretty quick otherwise [and seems more accurate than scanning text recognition, although I have an elderly copy of Scansoft's OmniPage [v14 Pro not the latest v16] - eerily also by Nuance - que X Files Music].
Generally programs such as these allow a few activations before the Nuance thought police take action - after which you have to beg for re-activation using the 're-installed Windows/faulty hard-drive/budgie's sick' excuses. More advanced DRM like Steam [games] simply allow you to install on as many PCs as you want, you just log-in via the internet [unlikely for Dragon software as Steam requires the internet for on-line gaming, whereas Nuance customers may not always have access]. However there is Dragon's 'installshield update manager' that installs itself in a basic Steam manner, although this doesn't do much until you register the software [won't update until then]. As Dragon isn't software I use regularly, being able to install on a few PCs [main PC and the laptop] seems reasonable. Can't find any licence agreement on the CD/PC though, so next time I'll have to read it during install before I click the 'just get on with it' button.