How to extract ZIP from self-extracting exe?

7-Zip should be capable of doing this. You can right click the file and select "Open Archive" or navigate to the file within 7-Zip and right-click and select "Open Inside".

On Linux it is possible with "zip" utility:

$ file london_f.exe
london_f.exe: PE32 executable for MS Windows (GUI) Intel 80386 32-bit

Warning: The next line changes the original .exe file to make it a pure zip archive without the exe parts!

$ zip -J london_f.exe
$ file london_f.exe
london_f.exe: Zip archive data, at least v1.0 to extract
$ zip --version
Copyright (c) 1990-2008 Info-ZIP - Type 'zip "-L"' for software license.
This is Zip 3.0 (July 5th 2008), by Info-ZIP.
Currently maintained by E. Gordon.  Please send bug reports to
the authors using the web page at www.info-zip.org; see README for details.
...

If you're dealing with gog.com games, use Innoextract. unzip, unrar, 7zip and others did not work for me:

sudo apt install innoextract # Install (On Debian/Ubuntu)

innoextract setup_duke3d_2.0.0.85.exe # Extract