Hm... in many cases it might be a better idea to dump memory into a binary file instead of text...? Then you can examine it using a hex editor (if you know what you are looking for) or load it in a disassembler if you want to analyze the code parts.
But if you want to examine the game code, try loading it in a disassembler directly. And use the Dosbox debugger. It's somewhat minimalistic but so is everything under DOS.
Although, now I recall someone mentioning a Dosbox plugin for IDA. But I don't know if it's still being developed, or if it works with the free version.
My favorite disassembler is Ghidra because I find it much more user friendly than radare2, and unlike IDA, it doesn't require $$$ when you need features that aren't included in the free version. (BTW, I think DOS executable support was removed in freeware v7, and even v5 doesn't properly disassemble all formats.) Some people steer clear of it as it was developed by the NSA. But I've been pretty happy with it.
Some people seem to recommend Hiew (a hex editor with a disassembler engine) but I've never used it.
I'm a newbie in the field of reversing so this is just my 2 cents. 😜