I have Audioengine A5+ speakers connected to the main output of a USB audio interface, which is in turn connected to a Windows computer on the LAN. Could I share this USB audio interface with another Windows computer on the same LAN and send audio from that computer to the same external sound card?
Depending on your latency requirements, there are a wide variety of network audio protocols that may suffice for this application. Essentially, both computers would have "virtual sounds cards" which pipe to and from the network. Specifically, you want layer 3/4 protocols that will operate with standard COTS networking equipment.
Examples of these protocols which are open standards are AES67, Ravenna, and NetJack. There are also proprietary protocols like Dante and Q-LAN. There are also layer 2 protocols like AVB and others, which I would avoid, as their "layer-2-ness" makes them more difficult to work with.
In any case, find a virtual sound card for one of those protocols, install it on both machines, route your source into the sending device, and then (on the other computer) loop the output of the virtual soundcard back to the real sound card (driving the speakers).
MS Windows provides network sharing of printers and hard drives, but I see no evidence that it supports sharing any other kinds of resources or ports or interfaces. It is technically possible, but doesn't appear to be supported by the operating system. That doesn't mean that there might be some way to implement it with layered applications.