GPU does not support DirectX 11.0

Your Windows does have DirectX 11 installed but the GTX260 does not support DX11 features.

I really doubt this would work but some games can be forced into DX10 mode using DXCPL

http://steamcommunity.com/sharedfiles/filedetails/?id=264396486&tscn=1401340607

Similar situation but I play GW1 with Direct3D 11 just fine; is that not DirectX 11? Card is Quadro FX 770m.

Quadro FX 770m is a DirectX 10 card.

PvZ:GW1  requires DirectX 10.

Windows may have a higher version of DirectX installed but it's extra features aren't usable by the hardware.  It's backwards compatible with older versions.