Where do companies get miniature GPS electronics from?
A quick search lead me to a TI part: TC6000GM datasheet. The chip is 9.3x10mm, not very small but not big at all.

So yeah, regular people can buy small GPS modules in seconds... But can a regular person fit it in a watch, together with the battery, the display and all the electronic needed to run everything? No.

First of all a single person, even a very good professional in the industry, cannot design such a system on his own in a reasonable time frame. A lot of effort goes in integrating all the parts in such a small case, letting them talk together properly. Plus a big company has great leverage to the ICs companies.

Let's say you are Samsung and go to Stackexchange Semiconductors inc., and tell them you want to make 10 million smart watches. You can ask SS to make you a chip that integrates:


the battery charger
the dcdc converters
the cpu
the gpu
bluetooth
memory
gps
accelerometer
...


Integrating all this in the very same die is not possible because tecnology differs a lot for digital, RF, MEMS, power and so on. It is possible to include many dies in the same package, usually done for the CPU to include the memory, for an high price and a lower yield.

You can also go as far as to require a certain pinout so that routing on your tiny pcb is easier. I expect a smartwatch to include an handful of chips, not more than five, and many of them are probably ASICs, i.e. application specific integrated circuits, built only for that very specific platform. This is possible only because you are guaranteeing you will be buying 10 million parts.

Why don't big companies just use regular chips you can find on RS or whatever? Well, sometimes they do, generally to save money, but it is a compromise because you cannot achieve an high level of integration without defining precise specifications for each square millimeter of silicon you are going to include in your product.

As an example, think of antennas. A Samsung engineer finds out that he can integrate a thin foil oddly shaped GPS antenna in the watch body, but unfortunately the impedance does not match the requirements of the generic solutions on the market. An impedance matching network using discrete components is a no no because there is no room on the PCB, so what is the solution? Have a company make a chip that fits your needs.

You could try building a watch using regular open market products, but you will probably end up with something more the size of a smartphone, if you are very good, and performances would probably be sub par with respect to an heavily engineered product.