Greetings Vojtěch. Welcome to the Temple of the Roguelike.
First, I view you making the statement blind people find roguelikes hard to play after trying only two yourself (ZAngband is almost identical to old Angband on terms of user interface) as a very unfair generalization. That said, I think only classical games of this genre can be effectively played using screen reader and these are in decline recently.
Here are a few games that do feature useful support for screen readers.
ADOM: Regarded as quite accessible, due to verbose descriptions, excellent look command and many status changes being also reflected in log. There has been
interesting discussion on rgrd about that.
DoomRL: Features specific enhancements for the blind. Besides ADOM-style looking it has two commands - examine monsters and examine items, which report information by giving relative locations. I heard there is also a mode which can disable the map and give more info by text, but I do not know how to activate it. Furthermore, DoomRL has meaningful in-game sound which is rare thing for classic roguelike.
Warp Rogue: Now defunct, but features the most enhancements for screen readers. Copx is truly the champion here, see the
rgrd post for all the things he did.
I know of only one game that can do kind of state dumps, and it is ADOM again. There is a command to save verbose log file of character. The file contains all kinds of data, but only a screenshot for the map.
I doubt there is anything in existence that exposes the data structures in readable way. There is just no reason for game developers to do so, because it would mean maintaining another data output for zero gain. When anyone thinks of blind players they implement convenience features right into the game. Your best bet to get state information about a game is to modify the source code to add this. But then, if you can program well, you can improve the interface directly which is more effective option. Also, I think reading game's interface is not as bad option as you make it sound. Roguelike library Necklace of the Eye does just that and is very successful at providing alternate presentations for many games.
I am going to post about captcha in website related subforum shortly. Maybe Slash can do something about it.