Hi byrne,
As you can see from the documentation, DatePicker is not supported in WinJS, however the document also suggest you use select and options instead:
Unsupported WinJS APIs on Windows Phone 8.1
If there is too much workload for you to create your own style DatePicker, you can either choose some third party code library as a assistant.
PS: the screenshot you are using seems to be a C# version.
--James
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