I have read the FAQ on this at https://winscp.net/eng/docs/faq_fxp but it misses the idea. WinSCP would act as a "middleman" in this case, loading the file from the source remote server into memory, and feeding it to the target remote server. You could even do this at the same time potentially.
Yes there are all sorts of network caveats associated with this but it's still feasible.
For comparison, the command line SCP command does support remote servers for both source and target arguments. For example:
scp email@example.com:/home/bob/myfile firstname.lastname@example.org:/home/alice
scp process on local serves as a conduit between the two remote servers. WinSCP should be able to do the same.