I created a chatbot using dialogflow and I added a website link to the response, I have integrated the bot in Telegram and the website link is working perfectly, but on the web
Sadly the web demo only supports plain text responses, so adding an clickable url within your chatbot for the webdemo isn't possible. Luckily, this is a limitation for web demo, so any other integration that do support URL's in their chats will work as you have seen with Telegram.