This encompasses at least 2 critical aspects (which might be worth documenting as 2 new issues):
set the HTTP headers to match the headers sent by a well-known mobile browser (at least the User-Agent header, possibly others such as the "Accept" header)
make phantomjs interpret the Web page as a mobile browser would; in particular, using the notions of "viewport" that is so far specific to mobile browsers
Both of these would benefit from being imported from "profiles" of virtual browsers that would include the said headers, the dimensions of the underlying device, the dimensions of the viewport, etc.
This encompasses at least 2 critical aspects (which might be worth documenting as 2 new issues):
Both of these would benefit from being imported from "profiles" of virtual browsers that would include the said headers, the dimensions of the underlying device, the dimensions of the viewport, etc.