Define "completed". For rules purposes (AFAIK, I don't work for the league), a trade is official when all parties submit their paperwork to the league office.
If Winnipeg did that on their end but Toronto didn't until after their game, this was kosher, as the trade is not official until Toronto's paperwork is in (even if it's been agreed to). Would have sucked if O'Shea informed Willy and then the trade was cancelled due to Heath getting injured during the game, though.
If Toronto did submit the paperwork before the game, then he should not have played barring some weird wording everyone agreed to making the trade only take effect after the game.
Given the commish's crackdown on personnel rules, I figure they'd look at it if it wasn't on the level.