OK, your system uses TimeSpan, but in this case you should follow the suggestions:
Your code in the EditorRequired event is bad, the type of the timepicker editor must be GridTimePickerEditor().
sender, Telerik.WinControls.UI.EditorRequiredEventArgs e)
|| radGridView1.CurrentColumn.Name ==
On the other hand, unfortunately, at the moment the GridTimePickerEditor does not contain DataTypeConverter property (or I just don't see).
Because the type of the Value property of the editor must be DateTime, you have to convert your original TimeSpan type value to DateTime before you write the Value property.
And, when you read the Value property, the type of it DateTime, you have to convert it back to TimeSpan.