I agree with all samples posted here but I think you are little confused because of completely different "Template" model of "Data" in WPF against pure closely bound UI + Data model of WinForms.
Coming from WinForm to WPF is little big learning curve, I myself took two years to start coding in WPF because I was always more comfertable in codebehind files.
My best guess is first you have to look into "Logical Tree" and "Visual Tree" concepts of WPF, where you will understand that how easlily WPF UI Elements and non UI Elements (Data objects) connects just in XAML without writing any C#.
And another most important concepts like "Triggers".
All you need to create is "Data" objects which will be your chess items (King,Horse) etc, derived from one common base class implementing IPropertyChanged interface and they will implement properties like "CanBeKilled", "IsPossibleTarget" which can be simply bounded in ItemTemplate of ListBox where your ListBox will hold current selection.
ListBox's item panel template can be one of the above examples and on MouseOver, you can highlight color or border according to above properties. And all you have to do is, update Every item's boolean properties in ListBox when the selection changes.
I just read your Edit part and I believe the Code Behind must be different and simple in WPF because comparing with WinForms, nicely designed WPF will have 90% less code behind compared to WinForm.