Transfer between two PCs connected directly by Ethernet cable?

Is it possible to use WinSCP to transfer files between two PCs connected directly by a cross-over Ethernet cable? Wondering if this is a feasible solution for transitioning from an old PC to a replacement.

If the computer on the other end runs a file transfer server (FTP, SFTP, ...), then yes.

But you can also just use shared drive. Then you do not need WinSCP. Though WinSCP can work with shared drives too – just as it can copy between any two "local" drives:
https://winscp.net/eng/docs/task_file_management