Binding to viewmodel from inside a datatemplate
Command="{Binding RelativeSource={RelativeSource AncestorType={x:Type Window}}, Path=DataContext.StartVideo}"
Another approach would be to use ElementName binding instead of RelativeSource.
Example:
<Window x:Name="root" ... > ... Command="{Binding ElementName=root, Path=DataContext.StartVideo}" ...A possible advantage over RelativeSource is that this is explicit; if someone changes the XAML hierarchy then relative references could break unintentionally. (Not likely in this specific example of binding to a Window however).
Also if your "root" element already is named then so much the better it is easy to take advantage of.
It is also somewhat more readable.