How difficult is it to adapt and run a modern browser engine on DOS?

Question

Browsers

For example, the same blink, and file a simple browser based on it

Answer 1

You can :)
You need to know perfectly not only the work of DOS (there will be no particular problems with this, there is a lot of literature, the sources of FreeDOS or an analogue can be found without problems), but also the work of the desired engine. Because you have to do a lot of things yourself.
Fan project. People do not do such nonsense - they even write programs on brainfuck :D