I still can use Applixware from good old libc.so.5 days (I think this application is about 5-6 years old). It works. Nothing more. The programmers made a good job and wrote an application without using internal interfaces or something else.
Also an a.out linux distribution (SuSE 4.2) runs nicely on the x86-64 kernel (except for GNU emacs 18 who doesn't like 4GB of address space) I also ran some very old a.out binaries from Linux prehistory (~1992) successfully on the x86-64 kernel.
If your Windows application uses internal interfaces or is build in a wrong way, it will fail with the next Windows version, too. The same is true for Linux. There is no difference.
Win64 dropped supported for 16bit Windows programs. Wine on x86-64 linux runs them still fine. -Andi