sublime's behavior with respect to this is pretty weird.
I'm on windows 7 and I find that with one font, only gdi will give me bold and italic, with another font, only directwrite works. With some fonts, either will work, with others, neither will work. If you only have the bold or italic version of a font, sublime will fake the missing italic or bold version, respectively, unless it does not like the font for some reason, in which case you get neither bold nor italic. It's pretty baffling.
(I verify that bold and italic of these fonts work in Word, and that Word is really the bold and italic versions of these fonts and not "faking it" because for example, the italic f of certain font has a distinct look from regular f.)