Is it possible to have someone only having the rights to monitor the chat, without being presenter?
Yes, that is an option.
You will have to enable some of your participants to be able to monitor and use the chat instead of you.
In order to do this, go to Manage People button and click on the three dots next to the name of the person you want to make an assistant.
On the drop down select the option Make Assistant.
As soon as you enable this for that user, they can manage the chat for you.