The existing web demo integration in Dialogflow is quite limited in terms of capabilities. For example, you cannot display clickable hyperlinks inside the chat window.
What is Rich Webchat?
Rich Webchat is a system for rendering rich content and rich controls inside a chat window when building web based chatbots using Dialogflow.
Things like clickable hyperlinks, text formatting, line breaks, bullet lists, images are rich content. For example, this screenshot of an interaction with the demo SupportBot on this site shows the chatbot rendering bold headings, images, clickable hyperlinks and line breaks.
Things like buttons, list selectors, carousel selectors etc are rich controls. My Gift Minion demo bot includes some rich controls like carousel selectors and buttons.
In my free "Rich Webchat using Dialogflow" course, I explain the system you will use to create chatbots with these such capabilities.