Toys and gift packaging are usually made up with more than one material; they could have plastic, cardboard, paper, etc. The material should be segregated and put in with other recycled items as without segregating it would be difficult to recycle.
Few companies use only eco-friendly and recyclable packaging. The gift bags can be reused as they look pretty and are usually reusable. The gift boxes can be upcycled with the help of various online DIY sites.