Recent versions of rsyslog do not use /var/log/syslog but /var/log/messages instead. It might be useful to update the default /etc/logcheck/logcheck.logfiles to reflect this change. This would make it working "out of the box" again. I do not know the default logfiles of other syslog implementations like syslog-ng though.
PIng?
This is still valid with latest version, I will CC syslog-ng maintainer to see if this change to "messages" wouldn't cause breakage for them
[master f08e0bb82c57] app-admin/logcheck: Handle /var/log/messages (#531524) 1 file changed, 62 insertions(+) create mode 100644 app-admin/logcheck/logcheck-1.3.18-r1.ebuild