Add-in functionality changed again between Office 2007 and 2010, to support new features like the changed UI (RibbonBar). The addin you created for Office 2010 uses features that did not exist in the Office 2007 apps (Word/Excel etc).
Office Add-ins are typically forward compatible only. That is future version of Office support older older plugins, but the opposite is simply not possible as new features get added all the time.
e.g.
- Write an Office 2007 addin and it will likely work on Office 2007, Office 2010 and Office 2013.
- Write an Office 2010 addin and it will likely work on Office 2010 and Office 2013.
- Write an Office 2013 addin and it will likely only work on Office 2013.
Please note that while they "work" they will often look very old-fashioned as they typically use the older UI elements and not the latest version.
Create a 2007 add-in instead
If you really need Office 2007 support, you need to create a 2007 Add-in instead (as well?). Otherwise you will likely be using features that simply do not exist in Office 2007. The only possible (unlikely) alternative is to add Office 2010 DLLs to the machines, but as you are then effectively upgrading Office I doubt that is legal without a Office 2010 licence (so you might as well upgrade them anyway).