Using logrotate to only compress and delete old files without rotating
Replace
/var/log/management/abc.log.*[!.gz]
with
/var/log/management/abc.log.*[0-9]
Your combination of dateext with an empty dateformat is a nice way avoiding additional numbers in the filename!
When somebody else finds this answer, the next line is important:
nocreate
And when you want to delete these files after 60 days, use
postrotate
find /var/log/management -name "abc.log.*gz" -type f -mtime +60 -exec rm -f {} \;
endscript