Yes. Adobe licenses typically extend to one copy on your main work box + one other. If you get a 3rd computer later, you'll need to de-activate one of your current installations.
Elements is not part of the Cloud, it is a standalone program... but the license is the same... 2 computers
Cloud License http://www.adobe.com/legal/licenses-terms.html
When you have future questions, use one of these links... and mention PHOTOSHOP Elements or PREMIERE Elements
Photoshop Elements Forum http://forums.adobe.com/community/photoshop_elements
Premiere Elements Forum http://forums.adobe.com/community/premiere_elements