I've been playing doom for a while now. I think I should tell you about how do make things easy.
1. Get rid of your DOS emulator.
2. Get GZDoom
here. It's a very good source port. It comes in a zip package so make a source port folder for it.
3. Get DOOM 2 on steam. Goto the file location of doom 2 in C:\Program Files (x86)\Steam\steamapps\common\Doom 2. Once you have that done? Extract the IWAD (DOOM2.wad) into the source ports folder.
4. Click gzdoom.exe & rebind controls and you're ready to play.
chromebook
Since chromeOS doesn't support windows apps, my best bet is for you to try downloading a linux mirror.