Looking for a *fun* way to introduce basic electronics to my kids
I would stay away from anything so complicated that you only can use it as a black box, like in the video a USB interface. Instead I would use very basic components, preferably things which generate a sound or display something, these will appeal to your youngest too.
One possible project is an electronic die. You can do this with a few HCMOS ICs, like a 7-segment LED driver. It has the advantage that you don't have to introduce transistors yet (transistors are Really Complicated Devices!!) and they see something happen.  

edit (re OP's comment)
HCMOS is a family of digital ICs, it comprises basic logical functions like gates (AND, OR, NOR, inverter,...), but also more functional blocks, like counters and the 7-segment driver I mentioned. For the die I was thinking of an oscillator you can start-stop, which makes the counter loop from 1 to 6. (Note to chief engineer: that's a presetable counter, a normal counter would start counting at 0.) The 7-segment driver converts its binary input to a pattern for the 7-segments digit display.
Alternatively, you can create a die-like LED pattern and use logic ICs to determine which LEDs have to light up for which counter value. (chief engineer: you can use a Johnson counter, like the 74HC4017. Count from zero to 5.) For instance, the center LED only lights up when you roll a 1, 3 or 5. Then you OR outputs 0, 2, and 4 of the counter (remember, zero-based)
The advantage of working with logic ICs is that you don't need to explain about electrons right away, and that they can get acquainted with voltage levels first.
If you create the oscillator with a NAND gate like the 74HC132, you can explain its working with the water model: voltage = water level, capacitor = water tank, resistor = thin water tube.  

For a concrete example see this googled document