The reason you can't use 16-bit assembly is because the 16-bit subsystem has been removed from all 64-bit versions of Windows.
The only way to remedy this is to install something like DOSBox, or a virtual machine package such as VirtualBox and then install FreeDOS into that. That way, you get true DOS anyway. (NTVDM is not true DOS)
Personally, would I encourage writing 16-bit assembly for DOS? No. I'd use 32- or even 64-bit assembly - the reason being there are a different set of function calls for different operating systems (called the ABI). So, the ABI for 64-bit linux apps is different to 32-bit ones. Not sure if that's the case with Windows. However, I guarantee that the meaning of interrupts is probably different.
Also, you've got all sorts of things to consider with 16-bit assembly, like the memory-model in use. I might be wrong, but I believe DOS gives you 64K memory to play with "and that's it". Everything, your entire heap and stack along with code must fit into this space, as I understand it, which makes you wonder how anything ever worked, really.
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