The eventstats command get the dc(dns) and assigns it to the totaldns field on every event. In the original query, you had a stats command to get count. The only field that remain after the stats command are the one's that are included in the stats command. So I added the max(dest_dns), (could have used anything, values, first, last etc.) only so the field carries over and can be used later. In the second query, since you do not have the stats command, you don't need the max piece. So try this
index=network sourcetype=nessus severity!=informational signature=*Windows* OR signature=*Adobe* OR signature=*Java* OR signature_family="Windows : Microsoft Bulletins" OR signature_family="Red Hat Local Security Checks" OR signature="Google Chrome*" OR signature="Firefox*" OR signature="MS*" OR signature="Flash Player*" OR signature="Solaris*"
| dedup dest_dns signature_id
| eventstats dc(dest_dns) as TotalDNS
| bin span=1mon _time
| eval PatchScore=cvss_base_score/TotalDNS
| eval Time=_time
| convert timeformat="%m-%Y" ctime(Time)
| stats sum(PatchScore) AS "Avg Host Patch Score" by Time
... View more