Reddit mentions of Bluecell 50 PCS Blue LED Electronics 5mm

You could actually make these pretty easily. You'd just need a blue LED, a photoresistor, and a couple of volts. I'd say go with an LR44 since they're cheap, small, a couple volts, and will lie flat in the shoe. Do the math or play around with them to see how many you'll need (Depends on how you set up the circuit, though I'm guessing one in each shoe will be fine).

So the circuit is pretty simple with the three circuit elements (LED, photoresistor, battery) in series. It's a little tricky though, since the photoresistor's resistance increases as the amount of light hitting it increases. So if you just wired everything up in series, the LED would turn on when it's light outside... that's the opposite of what we want. But you can make a voltage divider circuit and include the photoresistor in that, so that the brightness of the room and the brightness of the LED are inversely proportional, which is good.

Once you have the circuit, you just have to find a way to somehow put it in the shoe. Take the sole out, drill a hole in the tip for the LED, and drill a hole on the side for the photoresistor. Then lay your circuit flat inside the shoe, position the LED and photoresistor accordingly, and then glue them in so they stay in place. Cover the circuit with a strip of duct tape so it stays down, and then cover that with a Dr. Scholl's to maximize comfort and durability.

If anyone actually wants to do this, let me know. I've linked to the parts you would need, and they're all pretty cheap (the Dr. Scholl's are the most expensive part). I can draw up a circuit schematic if anyone's interested so then it would just be a matter of you soldering, drilling, and gluing it together.

Edit: Might also be a good idea to include a switch so you can save on battery life. There are all kinds of switches out there to choose from, and you can put it pretty much anywhere in the circuit where all the current flows through (so avoid putting it in the voltage divider section). So that part of the design is totally up to you. Maybe drill another hole in the side of the shoes for the switches, maybe have them be toe-activated, it's your call.

I don't know if those LEDs are what you want. I think those LEDs each contain a small controller, and that controller will cause them to automatically change color. You don't control the precise color, nor the speed that the colors cycle. You could turn the LEDs on and off by cutting the power to each individual LED, but that would probably reset the color cycle of that LED to whatever the starting color is. So you will probably end up with a jumble of colors.

If you're OK with just a single color, you could use solid color LEDs, like these. If you do want different colors, you could buy LEDs of different colors and statically arrange them in an aesthetically pleasing way. So the top might always be blue and the bottom might always be red, but maybe that's OK. If you need fine-grained control, you could use 4-terminal RGB LEDs, and maybe use static resistor values to control the brightness of each RGB channel.

If you want something that looks a lot like the video, you'll probably want to get an addressable RGB LED strip (depending on your need, you might need a few). This gives you a lot of control, but you'll also probably need a microcontroller to drive it.

There's also this, which is a RDG LED strip that has an embedded microcontroller, so you can drive it from USB. You can see from that page that they're trying to make simple animations easy.