How did you eliminate the ISP? Or some interim link to the game site, or even the game site itself?
Where did you purchase the Ethernet cables? What Ethernet cables/specs did you purchase? What is printed on the cable? There are lots of junk and fake Ethernet cables being sold everywhere!
Swap in Ethernet cables from a known working system without connection drops.
On your computer use Reliability History and Event Viewer to look for error codes, warnings, and even informational events that correspond with the times that the connection drops.
The router's logs (if available and enabled) may be capturing some related issues or problems. Who has full admin rights to the router? You will need help from that person.
Computer specs:
Add PSU: make, model, wattage, age, condition? History of heavy gaming use?
Disk drive(s): make, model, capacity, how full?