There are some other retro computer or consoles that could probably be just as useful for this. But DOSBox (as well as QEMU+FreeDOS, for those that prefer that) are nice because they have fully open source implementation from the CPU-level up to the user utilities, so there is no need to mess with dodgy ROM downloads or such to get things working.
Exposing a port isn't exactly a safe thing to do nowadays, and I'd be wary of the security posture of an "old phone". Proceed with caution.
Assuming you are using an old phone with termux to serve de webpage. What could be an attack vector?
The phone will be running Android 7.1