Hmm.. according to Linksys's site, drivers aren't being provided for DOS. However, with a bit of searching, I found a link regarding
OpenBSD/i386 that shows a list of
ASIX Electronics AX88172 based USB adapters (axe), including:
ATEN UC210T
BAFO BF-320
Billionton Systems USB2AR
Buffalo(MELCO) LUA-U2-KTX
Corega FEther USB2-TX
D-Link DUB-E100
Good Way GWUSB2E
Hawking UF200
Intellinet USB 2.0 to Ethernet (rev A)
JVC MP-PRX1
Linksys USB200M
Netgear FA120
Sitecom LN-029
SMC 2209USB/ETH
SnapPort USB 2.0 LAN Adapter
ST Lab USB 2.0 Fast Ethernet
Surecom EP-1427X-2
System TALKS SGC-X2UL
TRENDnet TU2-ET100
Z-TEK ZK-R01-2
So with this long a list, it may be possible to get an NDIS driver from another of these nics and use it for your Linksys adapter. It's the only thing I can come up with at the moment, but at least the chipset would be a match.