Are you sure that the other monitoring software is using exactly SNMP, not some proprietary protocol? Does it use standard SNMP port?
You can try capturing communication of that software to the router with Wireshark and compare what network packets it's actually sending.
also you can try getting some data via SNMP using snmpget package from netsnmp software https://sourceforge.net/projects/net-snmp/files/net-snmp%20binaries/5.5-binaries/net-snmp-5.5.0-2.x64.exe/download
You can try capturing communication of that software to the router with Wireshark and compare what network packets it's actually sending.
also you can try getting some data via SNMP using snmpget package from netsnmp software https://sourceforge.net/projects/net-snmp/files/net-snmp%20binaries/5.5-binaries/net-snmp-5.5.0-2.x64.exe/download