Is it normal to reach rooms where nothing appears to happen?

I'm playing the first quest in Zelda, and reached this point in the map.

...nothing appears to happen. Is this a glitch in the Zelda Classic "emulation"/"engine", or something that also happened in the original game? Do I need to do anything special to see what (s)he has to say or offer me?

It is actually completely normal for nothing to happen in many rooms in Zelda I, as it is a game predominately based on exploration. Check what the woman has to say, if it is nothing of interest, explore more areas on the map for the right direction to go towards completing the main quest.

Yes, this is normal. The woman will sell you stuff later once you have the proper item. You need a letter of some kind (looks similar to a map item you find in dungeons). Once you show her the letter, she will sell you potions that can restore your health.

The potions are quite helpful in later dungeons, which are quite long and difficult. By the time you get to them, hopefully you will have found the letter through exploration.