We need to think, not head to head, but rather what does physical space offer that digital space can not. Human interaction, human interaction with products. The best example this fan boy can think of is the Apple store whereby Apple needed to put their products into people's hands and have their experts work 1:1 with customers. This was a huge success. So how might Toys"R"Us do this?
Inventory Reduction for Greater Variety
I would start by reducing the store level inventory to make room for a greater variety of product selection. Use a order kiosk when inventory is unavailable with home or in-store delivery. Now you can bring in more exotic toys from around the world for that true one of a kind gift.
Local Toy Crafters
With the freed space, you can add local toy crafters on consignment to add additional flavor. You can feature a local crafters monthly like book stores have authors. This would be a great venue for startups that can't afford large rollouts. How many more crafters would want to sell their goods if they could much easier?
Have a toy craft shop where you can create your own toys, build models, take classes. Build a brand new game, or create a hand made classic. Don't just sell toys, sell the raw materials to create toys.
Help with patents, printing and manufacturing of games and toys to assist startups. No better way to get insight into the newest craze and have first access to them.
Thinking along these lines of crafting, consider How to Make a Gumball Machine (DIY) with over 356,000 views in under two days. People are very interested in these things. To spend time with their family doing fun projects.
The King of Random
I would consider sponsoring Grant to create some of his builds from Toys"R"Us craft supplies, and perhaps even do it on location with some customers in your Crafting Fun craft shop. Have all the designs available for download with links to the craft kit.
Consider those comic books and figurines? Entire stores stay in business with these comic books and figurines. Just don't have them available, have real experts there to assist. Have monthly mini-cons where you showcase a product line. Again, just don't set them on the shelf, Amazon can do that. Be engaging. Be fun.
Why not also look into antiques. Even host local toy auctions.
Consider the Human Interaction
In closing I want to reiterate the human interaction that can not happen online. What can be added that the digital experience just can't offer. How can you bring families together with gaming and toys? You can bring about a resurgence in gaming and toys of all sorts.