I can confirm from installing and running Atom on my own WSL system that there are two problems that you are running into. The first one of these is fairly common, but the Atom error message is so different from other applications that I'm glad you've posted it so that others can find it when searching.
/usr/bin/atom: line 195: 89 Segmentation fault nohup "$ATOM_PATH" --executed-from="$(pwd)" --pid=$$ "$@" > "$ATOM_HOME/nohup.out" 2>&1
That error is caused by your first issue. As mentioned in the comments, you are running WSL on Windows 10 without an X server.
WSL on Windows 10 does not support Linux GUI applications on its own. Linux GUI applications (traditionally) are X clients, which use the X11 protocol to communicate with an "X server" which handles the job of displaying them, translating your input (mouse, keyboard, etc.), and other tasks.
On Windows 10, WSL just doesn't (directly) support that functionality. There are really three possible solutions, and while I'll summarize them here, I'll point you to several other questions for the details:
Upgrade to Windows 11 where there is a new feature, WSLg, which directly supports GUI applications with both X11 and Wayland (the "successor" to X11).
Run a third-party X server such as VcXsrv on Windows 10
Run xrdp
in Ubuntu and connect to it via the Remote Desktop application in Windows.
See:
For an (admittedly overly) long and detailed comparison (performance, memory, ease of installation, easy of use) of the options, see my answer.
The other error
expr: syntax error: missing argument after ‘8’
Even with an X server installed, you'll still receive this error message for the moment. This is a bug in Atom. It's fairly harmless, it seems, and Atom will still run just fine with that error message. It occurs because Atom doesn't anticipate that you might not be running a session manager, which you don't need under WSL.
If you run via Xrdp, however, you won't receive that error, since you will be running under a session manager.
Regardless, nothing to worry about, and it is reported to be fixed in the next release anyway.