x64 asm ¿cómo configurar un puntero de función a una función _cdecl C y llamarlo?

First, you generally need to pop the registers in the reverse order in which you push them, i.e.:
push RBX, push RBP ... push R15 -> pop R15 ... pop RSI, pop RBX, ret. This will definitely break the caller of _asm_func.

Next you should look at the Convención de llamadas de Windows x64 what all is necessary to make proper function calls. It is very important to get all the requirements right, otherwise things can break and even very late in some else's code, which is not the greatest thing to debug.

For example, you don't need to save all registers. If the callback function destroys them, it will save and restore them itself. So no pushing and popping is necessary there, RAX can be invalidated anyway, no argument is being passed in it.

But then note this part:

In the Microsoft x64 calling convention, it's the caller's responsibility to allocate 32 bytes of "shadow space" on the stack right before calling the function (regardless of the actual number of parameters used), and to pop the stack after the call.

Entonces deberías hacer SUB ESP, 32 before your code, then ADD ESP, 32 antes de RET.

There is also the requirement for "stack aligned on 16 bytes", but you don't currently need to address that, because "8 bytes of return address + 32 bytes of shadow space + 8 bytes of next return address" is aligned on 16 bytes.

Additionally, the Windows x64 ABI has also strict requirements on exception handling and correct unwinding. As Raymond pointed out in the comment, because your function is not a leaf one (calls other functions), you need to provide a proper prologue and epilogue instead -- see aquí.

The temporary saving of RCX al comienzo de _asm_set_func_ptr es innecesario

Otherwise I don't see any problems there, though.

Finally, semicolons ; are not needed at end of lines in assembler files.

You're pushing a lot of registers before checking g_pFuncPtr, but you're not popping them back off the stack if it's not been set. If you push something onto the stack & then don't make the call and don't pop them back, your stack will fill up fast.

You MUST pop registers in the opposite order of pushing them, or you'll get back the wrong registers.

Last, don't waste time & CPU cycles pushing them at all unless you have something to do with them:

    CMP g_pFuncPtr, 0
    JE SkipCall

    PUSH RBX
    PUSH RBP
    PUSH RDI
    PUSH RSI
    PUSH RSP
    PUSH R12
    PUSH R13
    PUSH R14
    PUSH R15
    MOV RAX, [ g_pFuncPtr ];
    CALL RAX;
    POP R15
    POP R14
    POP R13
    POP R12
    POP RSP
    POP RSI
    POP RDI
    POP RBP
    POP RBX
SkipCall:
    ret

... and please - please... do read up on setting up stack frames and managing stack frames inside calls. C calls and ASM calls handle stack frames very differently from each other.