Is it correct that I just need to move the AppImage file to e.g.
/opt is not in the default path of all users, but
/usr/local/games is and seems the right place for your purpose.
... and give all users the permissions to execute the AppImage file ?
chmod 1" be enough permissions ?
chmod 111 file ... No, users will also need the reading permissions set as well i.e.
chmod 555 file is the minimum for what you want unless all the users are in the same group as the owner of the file where in this case
chmod 550 file will suffice.
Notice according to
man chmod "Omitted digits are assumed to be leading zeros" ... Therefore, taking what you wrote literally,
chmod 1 will actually translate to
chmod 001 denying all permissions from owner
user:group and leaving executable permissions for anyone else ... I already assumed you didn't mean to do that, but if you indeed meant to deny all permissions from the owner user and group, then the minimum for you is
chmod 5 file or more explicitly
chmod 005 file which will allow, ironically, only
Others to execute the file.