This is incorrect. You've described the older notion of a time crystal but that has been shown to be impossible here and here. That is, the egg cannot flip "as if by magic."

The experimental result is more like, you have a bunch of eggs. You (an outside source) flip all of them, then you let them interact with each other in a specific way, then you put them in a random potential (these are the specific details that aren't particularly important for the punchline). You repeat this process every 10 seconds. However, when you measure whether the eggs are upright or not at any given time, you find that they are flipping (unsurprising) but they are flipping every 20 seconds. This is the notion of a 'time crystal' that makes sense. You've done something to a system periodically, and the system is responding at a frequency which is not equal to the frequency with which you do stuff.

As for the application, honestly, I have no idea. This experiment is a very particular arrangement of ions trapped with lasers. At the most basic level, it will help us understand more about how nature works and is somewhat connected to some proposals for quantum memory