Conversations are not a competition
Unfortunately, a conversational narcissist fails to realize that there is no competition. They fail to understand that conversations are interactive. It involves sharing of ideas, opinions and feelings from both or all involved parties. It is not a one-way game where the narcissist will deliver an unending monologue. But it is not your job to make them realize that. The more you try to change them, the more you will feel stressed and anxious.
If someone who talks a lot about themselves makes you feel uncomfortable or frustrated, then the best thing for you to do is simply smile and walk away.
Here is an interesting video that you may like: