I am afraid, that will not work as a layer-style. You will have to draw the "arced rectangular" with the pen tool.... Best way to do this is to use Illustrator. You can then place the Text in PS an add layer-effects.
Still doable with Photoshop though.
Make your type layer and transform it
Convert it to a shape layer from the type menu
Select any of the shape tools to give you the fill and stroke options
Give the upper a layer a white stroke, and lower layer a black stroke. The black stroke obviously has to be thicker.
If it is not working right off the bat, click on the Line dropdown > More Options > Change settings to Outside and corners to Miter
Noooow I'm going to bed :-(
I'm pretty sure that this logo was created in Illustrator and not in Photoshop, you should move this question in the Ai section and of course if you have Ai.
in Ai you have a text tool that allows you to edit individual letters after using the arc text distortion ... in Ps you should type the letters separately in order to modify the "K" for example.
to get the same path in Ps you should duplicate the text layer 3 times (once placed the whole word with the "K" resized) ... change the color of the second level below to white and resize ... same for the third level below changing to black and resize.
this logo, however, is vector graphics.