A new walk-up feature has just been added to the My Disney Experience app which will now allow guests to join a waitlist to dine in real-time.
As you can see in the first screenshot below, there is a "Now" choice which will display restaurants near you that have an available walk-up list.
You can also choose a meal period or specific time to search and you'll see availability displayed for "today."
It should also be noted that not all dining locations offer a walk-up list via the app but may have walk-up availability. It's always best to check with the restaurant if there's a specific location where you want to dine that doesn't show walk-up availability in the app.
Lastly, in the screenshot below, you can see that Whispering Canyon Cafe has the availability to join a walk-up list and the wait time is estimated at 55 minutes currently for a party of 4. That can obviously change at any time.
Also, take note of the "Please move closer to the restaurant to join the walk-up list" advisory as there appears to be a limit of how far you can be from a restaurant in order to join.