On Tuesday I warned Target Corp. wouldn't succeed copying Wal-Mart Stores Inc.'s turnaround playbook. Unlike Target, though, Mcdonald’s's play-stealing plan is likely to work.
is a predetermined set of steps the player will perform, e.g. running left, then running right, in that way each player will know before had what all the other players will be doing during the "play".
In your usage, the "play" are the steps a company takes to perform a turnaround, it may be lower prices, firing staff, reducing opening hours.
"Play stealing" is simply the copying of the same steps from one company to another. The quote from the related article you've linked is
the plan was plucked directly from the playbook of Wal-Mart Stores Inc.
A playbook is book kept by the coaches of a team which contains ll their predefined plays.