It's a common thing for ND people to do as it allows us a a way to demonstrate empathy. The problem is that most NTs can interpret it as being off topic or making it about yourself. What they probably want in the conversation is to vent/express their emotions to another person. If you bring up a similar event that happened to you, they don't get that opportunity.
A good way to channel that impulse is to bring it up briefly and then immediately bring the topic back to them. Show them that you understand but still keep the conversation centered around them and their feelings.
"Hey, my mom died recently so I'm not feeling great."
"I'm so sorry, my mom died last year so I know what you're going through. How are you holding up, do you need anything?
Not NT but halfway decent at "translating" my thoughts into socially acceptable behavior.
It's okay imo. Great if you like stealth/sniper gameplay but it probably won't be the game to get you into it.