This adapter can already use vanilla AR8161 drivers as-is on modern Windows including WinXP and there are already guides on how to do so.

It seems the packet driver and NDIS2 drivers from this site can work with this network adapter after making some modifications, as this adapter is simply a rebranded AR8161 with a slightly different PCI device ID (E091 compared to 1091).

The drivers needed for this adapter from that site:
Packet Driver: L1FPKT.EXE
NDIS2 Driver: ATNDS2.DOS

The modifications needed is simply hex-edit the PCI device ID it expects for AR8161 to that of Killer E2200's. Open the driver files in hex editor and replace all mentions of bytes "91 10" (that would be 1091h) to "91 E0" (that would be E091h). There are 2 such mentions in L1FPKT.EXE, and 1 such mention in ATNDS2.DOS.

After this modification, the drivers should be able to pick up the adapter and initialize it fine, displaying its MAC address and link speed.

So far the Packet Driver works without any major issue. Tested with Arachne on FreeDOS and I could properly browse web sites with it.

NDIS2 driver can also initialize the adapter correctly, but I'm having trouble getting it working correctly with Win98SE. At best I could get the adapter detected and obtain IP address via DHCP but I could not ping anywhere nor access any website.

I've never set up NDIS2 drivers on such OSes before so I'm not sure if I accidentally messed anything up... after several failed attempts I managed to set it up correctly. Here are the correct steps AFAICT.
- Open Network settings, choose Add Adapter and select "Existing NDIS2 Driver". This installs base stuffs necessary for NDIS2. Reboot.
- After rebooting, open System -> Device Manager, the installed "Existing NDIS2 Driver" will show an exclamation mark, choose Update Driver -> Have Disk and choose OEMSETUP.INF from ATNDS2.DOS. This actually installs the driver to Windows folder and add necessary registry and PROTOCOL.INI stuffs. Reboot again.
- After rebooting, the NDIS2 driver as well as other stuffs in the chain should be properly loaded when "net start" is called, and "Atheros PCI-E Ethernet Adapter" should appear in the Network setting.

It seems Win98's network stack is different from present day Windows in that it kind of relied on WINS instead of DNS. And regarding pinging, at one point I did manage to get the adapter ping other places inside my local network but not anymore. Searched online about the issues and I got things like reinstalling TCP/IP and such (possible registry issues), but it doesn't appear to work... Again, maybe configurations are a bit different with NDIS2 compared to modern (e.g. NDIS4/5) drivers.