It's a script that starts with an EXE header ("MZ"). Having both EXE and ELF headers at the same location is obviously impossible, since they start with different bytes.
A possible, although very limited way to have an actual binary program execute on different platforms would be to create a DOS .COM file (which has no header, just the raw machine code) with a valid ELF header. It would then also work on 32-bit Windows via its built-in DOS emulator, and presumably on 64-bit Windows with WSL2.
The start bytes for a 32-bit ELF header decode as 16-bit x86 into:
7F 45 JG +45h
4C DEC SP
46 INC SI
01 01 ADD [BX+DI],AX
01 xx ADD ...
The first instruction is a jump past the end of the ELF header, unfortunately it's conditional. But we have 9 reserved bytes to continue this code, which is enough to undo the effects of the DEC and ADD instructions and then jump to the same address. I've written a 138 byte "Hello world" that works on Linux, DOS and also CP/M-80 that way.
It's possible to have the code that executes under Linux be a small (less than 2K bytes) loader program that creates 16-bit code and data segments and installs a handler for SIGSEGV. It can then jump into the same code that would run under 16-bit DOS, trapping every INT 21h and translating the most important syscalls into their Linux equivalents, kind of like a minimal version of Wine.
I have a proof of concept for that, it only handles the "read", "write" and "exit" syscalls, which is enough to write something like rot13 or hexdump. With a lot more work, it could be possible to produce really non-trivial software that runs in such a restricted environment...