I have used the jQueryUI spinner example to show that adding 'type="number"' causes a double set of up/down arrows to be displayed in Safari 6.0.2 and Chrome running under Mac OSX 10.7.5. There seems to be not only the jQueryUI set of arrows but also a native set of arrows. No problem with Firefox.
Since the spinner does not support "type=number" I think it would be reasonable to add that information to the "Additional Notes" part of the documentation. i.e. this is at least a bug in the doc ;-)