Since your Step 3 says "Search in "search applications", but didn't see "clash for windows"", you might need a Categories= in your .desktop for it to show up. Not sure how Chrome Apps shows up since the .desktop files for it doesn't have a Categories= line.
You can see https://specifications.freedesktop.org/menu-spec/latest/apa.html to determine what category you want to set your .desktop file in.
Note: Categories= is not needed if the file is actually in the $HOME/Desktop directory.
As a test, I have a Whatsapp.desktop file that I will use for an example. It looks like the following:
[Desktop Entry]
Version=1.0
Type=Application
Name=WhatsApp
Comment=WhatsApp
Exec=google-chrome --app="https://web.whatsapp.com/"
Icon=/home/terrance/.local/share/icons/WhatsApp.svg.png
Path=
Terminal=false
StartupNotify=false
Categories=Network

If I remove the Categories=Network line, we can see it no longer shows up in my menus:
terrance@terrance-ubuntu:~$ cat .local/share/applications/Whatsapp.desktop
[Desktop Entry]
Version=1.0
Type=Application
Name=WhatsApp
Comment=WhatsApp
Exec=google-chrome --app="https://web.whatsapp.com/"
Icon=/home/terrance/.local/share/icons/WhatsApp.svg.png
Path=
Terminal=false
StartupNotify=false

So, in your case add a line at the bottom that says Categories=Game and it should now show up.