I don't know much about shares, but for every winner must there be a loser?
if you're ignoring dividends or looking at something like futures, options etc.. then essentially yes, ignoring commissions the total money won and total money lost equal each other... thus some might say it is a 'zero sum game'
if you include commissions then it becomes a less than zero sum game - with less money taken out in profit than put in in losses
though with shares you've also got dividends which changes things significantly... technically you'll get short term price changes around dividends but in the long run they'll have an impact and IMO it isn't a zero sum game