At the moment only a Windows Version exists.
The Backup free Edition is the same code base as the paid versions. So it profits from the main software fast release cycles and immediate supports new VMware and Hyper-V Versions.
Yes, an appliance is very easy to deploy but in my eyes a security problem in an organisation. You are at the mercy of the vendors (security) update deployment.
So I think the idea behind Windows Version is, easy to use (everybody knows Windows) and integrateable in your existing patch, antivirus and monitoring environment.
If Veeam will add appliance or Linux support I think it will double/tribble nearly R&D and Quality control effort and will slow down release cycle.
I´m not from product Management from Veeam, but I think you will not see Backup free edition as appliance in the next time.
On MS licensing perspective, you can use Backup free Edition also on a Workstation OS (XP-8.1) on a PC/Notebook/VM. But for VMware vSphere 5.5 Support you need a 64bit OS.
Best reagards... Andy
EDIT1: You can add a feature request on http://forums.veeam.com . Veeam product management is very active in the Veeam Forums and the Forum will influence the priority list.