Basically it has to run on a fairly clean Windows machine. The competition will usually publish the specifications of the machine ahead of time and what's on it. What you enter has to fit entirely within the bounds of the competition, but can use anything else on the machine if it's available. So you could enter say, a 4kb entry, and use a bunch of Windows .dlls for icons or something as artwork, but you couldn't enter a 4kb executable and 100MB of libraries and other stuff.
For some languages where this is really hard to achieve, they'll carve out a separate category for a language if they think there will be enough entries. e.g. a Java category where the entry fits with the space limit, but can use any other library in the default Java classpath, even though that's very very big. Likewise for different operating systems (Linux, MacOS competitions).
There's been a fantastic resurgence in retrohardware and a category called "old school/skool" for entries that have to run in MS-DOS -- which can be ultra hard as you have to code up a lot more of the runtime libraries like music, graphics rendering pipelines, etc.
Its only the output binary size that matters. If the libraries are in there then it counts. Where it gets a bit funny is graphics libraries and gpu features. You wouldn't include vulkan in your size but you get a bunch of features that weren't available on older hardware.
