Is it possible to set a custom environment variable, which will be accessible from any other plugin, the same way as $platform and $path works?
There is a package EnvironmentSettings by Daniele Niero, but it seems my task is simpler and therefore there is a probablity that there is no need to dive deep into its code.
In Sublime, any plugin can modify the global process environment through os.environ from the Python run time. All plugin code runs under the same process, so once one plugin sets an environment variable, any other plugin could access it. I would imagine that this is how the package that you linked to in your question modifies the environment.
A simple example of this in action can be found in Default/exec.py which you can open by using View Package File from the command palette. In the __init__ method of AsyncProcess() there is code that modifies the Sublime process environment if you pass the path argument in your sublime-build file.
A simple example that you can run from the Sublime console would be the following snippet. Once you execute that code, any plugin that you create can access os.environ["MY_VARIABLE"] to see the value.
import os
os.environ["MY_VARIBLE"]="Some Value"
With that said, in Sublime $platform is not an environment variable, it's a special variable that Sublime knows how to expand itself which is divorced from the system environment outlined above.
A complete list of such variables can be viewed by executing the following code from the Sublime console:
from pprint import pprint
pprint(window.extract_variables())
The list of variables you get and their content depends on application state (platform, whether there is currently a project open in the window, the current file, etc).
The names of the variables that this returns are hard coded in the Sublime core and can't be augmented, so if you wanted extra variables here you would need to communicate that to other plugins and they would have to be modified to know how to use them.
From the sounds of what you're trying to accomplish in the comments on your question, what you want might be a sublime-settings file that contains a setting that specifies the directory to use for file actions in your custom plugins. If they all load the settings file to get the path you can modify the location in the config and have it take effect immediately. Alternatively you could do something like a top level module variable in one plugin and import it into the others.