Hmmm. So several points there:
1) Must include Text Inputs & Textareas
That is indeed included in the download for Range Slider and
it's a part of what you see in the example there - I didn't go
and uncheck anything. So I don't think this is the issue.
2) Input type should be something other than range
That would suggest the Example Code for Range Slider is
wrong/broken. But, this can't be right because the full jquery
mobile renders things properly, displaying the overall control with 2
text inputs, even though HTML contains type=range.
So that gets us closer to the real problem: Something else is
needed for Range Slider to properly switch those input type=range tags
to type=text.