OK, I tinkered with your 9 patch.
I must say it was poorly designed (72 dpi, while it should really be 320 dpi).
So, I redesigned it (you can see I moved the black pixels) and saved it to 320 dpi (in the drawable-xhdpi folder).
It seems it scaled well at ldpi and mdpi screens (so, I guess it will also scale well at hdpi):
The patch I used is this: