I agree that "sportive" should mean mischievous, cheeky, as in these examples:
I am not accustomed to sell things, sir, replied Lorna, who did not like him much, else she would have answered sportively, What is it worth, in your opinion? (from Lorna Doone)
http://www.litfix.co.uk/blackmore/lorna/chapt...We would not, however, be supposed, by these allusions, to imply that all the
papers of the Idler are light and sportive ...(Samuel Johnson)
http://www.gutenberg.org/dirs/1/2/0/5/12050/1...Then there grew up between them an affected opposition and indifference, and
a kind of half-sportive, half-earnest wrangling about trifles ...(After the Storm)
http://www.gutenberg.org/dirs/etext03/ftrth10.txtI think that "sportive" is often used as a synonym of "sporty" these days though, perhaps because "sporty" sounds rather informal, or because of the influence of e.g. French, especially in advertising:
Acoustic design for sportive people: Sports halls and gymnasiums are purpose-built for games, exercise and intense physical activity ...
http://www.ecophon.co.uk/templates/eco_newsit...Gore Sportive Ladies Jacket
http://www.gbcycles.co.uk/eshop.asp?wce=RCGO0...Are you looking for a versatile bike that reacts sportively while allowing
you to reach your potential at your own pace?
http://www.cyclestore.co.uk/productviewer.asp...Princess Aurora is the German Olympic bronze medallist Mandy Woetzel, who is
tiny and sportively built
http://www.telegraph.co.uk/arts/main.jhtml?xm...