They're Not Toying Around with Bankruptcy

They were once the Amazon or Walmart of toys and baby products but have been taken down more than a few pegs by the bullying from their rivals. "What's good for the goose is good for the gander", as is said. I suppose it's not child's play, or is it?

Is bullying from their rivals another way of saying failure to compete in the market?

Yes, "bullying" was supposed to be a metaphor for subduing their competition, for "toys R Us" rose and became numero uno in the toy and baby market by under pricing (bullying) their competitors until they dominated their area of the market, which is basically what Walmart and Amazon came along and did to "Toys R Us": rendered them unable to compete, by under pricing and capturing the online market for such items.Their "rivals" = Amazon and Walmart to be clear.