DNS question with cpanel, regarding subdomains...hard to explain

Are the two servers both using cPanel and WHM?

Are the two servers both configured in a DNS cluster (setup via WHM)?

If the second server is not using cPanel and WHM, you could at least use your cPanel/WHM system to create the sub-domain A record in the DNS zone, and then manually configure the second server.

If both systems are using cPanel and WHM and configured in a DNS cluster, then you could use the second server to either park the sub-domain on an existing account that hosts the desired files involved, or create a new account (e.g., via WHM access) using the new sub-domain as the primary domain name.

 

I would consider using the existing parent DNS zone to setup the new sub-domain, that is, using the DNS zone of "cursors-4u.net" to add an A record for a new sub-domain "cur" pointing to the desired IP address. Modifying an existing DNS zone may be performed using the Edit DNS Zone feature in WHM DNS Functions, as accessed via the following menu path:
WHM: Main >> DNS Functions >> Edit DNS Zone

Additionally, in cPanel 11.25 it is now possible for end-user cPanel accounts to modify DNS zones via the following features:
cPanel: Main >> Domains >> Simple DNS Zone Editor
cPanel: Main >> Domains >> Advanced DNS Zone Editor

Regarding the screen-capture image pointing to the name servers; it is normal for NS records to be automatically included based on the current configuration (e.g., as setup via root access in WHM).

When I view the infoDNS results page I see just one error (highlighted in red):

Code:

ERROR: One or more of your nameservers did not respond:
The ones that did not responded are: 67.255.195.88

The error indicated means, as its wording suggests, that the name server at the specific IP address did not respond; this type of issue could be escalated to your upstream host or data center as they would have direct access to your server(s) for troubleshooting. I'm not seeing where the IP was obtained from, unless it was from an earlier version of the DNS zones involved and cached by intoDNS:
InterNIC Whois Search Results | Nameserver: ns1.mmofam.com
InterNIC Whois Search Results | Nameserver: ns2.mmofam.com