It's blurry because it is not black and white, or rather there is a huge grey scale between black and white that sometimes can be considered analog and other times can be considered digital depending on the application.
In reality everything, except perhaps at the atomic level, is actually analog.
Digital circuits are actually analog comparators, usually with some hysteresis, that makes them flip their outputs depending on what the input voltage or current does.
Once you have such a "gate" you can combine them in an infinite number of ways to produce more complex logic functions.
Some devices, like simple latches etc are purely logic gates. Others are hybrids that contain both "digital" and analog circuits.
A simple transistor can be used either as a current amplifier, or it can be used as a switch. Or more accurately, a transistor has three states, Saturated (ON), Reverse Biased (OFF), and Linear (neither on nor off). As such, which mode you are using is dictated by how it is driven and arranged. When you are using it as a switch, using the On and Off states, the transistor always has to goes through that linear region during the transition. So yes, the definition is blurry.
As for your indicated device. It falls into that hybrid category. It takes digital inputs and outputs analog voltages based on those inputs and what the load is doing.
In the end, as Andy pointed out, it usually doesn't matter what you call it.
There are some exceptions though. A good example of that is a multiplexer, a device that channels inputs to outputs based on come control signals. A digital multiplexer is very different from an ANALOG multiplexer.
These are most likely a microcontroller, a voltage regulator and three full-bridge amplifiers.
First thing to check is connectors, loose cables, and on a cheap PCB base material as this, broken eyelets and traces.
The voltage regulator near the battery input is sure a standard IC, find its number and then the datasheet, then check if there is the advertized output voltage when the battery is connected.
Last thing to check is the crystal. Does the µC has a clock? For that, you need an oscilloscope and a 1:10 probe (or simply hold an 1:1 probe near the crystal pins). You should see an oscillation. If not, or only unreliably, the crystal may be subtly broken due to mechanical shock. It's not unusual for toys.
If all that works but the device doesn't, I would give up. No sense in putting more research into that cheap thing.
(I doubt one of the bridge amplifiers is broken, because then, you simply couldn't move backwards or forwards or steer, but the other function would work.)
Best Answer
There can be several reasons.
It is easier/cheaper to use standard packages than custom ones. So if you need 4 pins, but there is a standard package with 5, you have one spare. With large packages you can have many spare pins. Removing the pins or designing a package with a custom number of pins would be very costly in terms of set-up.
They may have been used during development/testing
You might have different versions of the same series part. Some in that series might have more pins than others, so the ones with fewer pins have N/C's
You might want an oversize package for thermal performance (or size of die), and as a result you end up picking a package with more pins than you need.
The chip manufacturers packaging factory may only support a few different packages, so there may not be one available with the correct number of pins, so you go up a size.
There are probably many more, but my fingers are tired.
You may then ask, why not just connect them to something? Well, that requires more time wire bonding. It also means an increase in silicon size if you have to add the additional bond pads to the die. There may be performance related issues with bonding the extra pins (stubs in high frequency circuits?). And so on.