Does the IBM Watson question answering system that won the Jeopardy game in 2011, support dialogue with users in its new versions?
I think you are referring to Watson Assistant, which is the 4th generation Q&A / Dialog / Conversation / Assistant service.
You can find a demo at the bottom of the page at https://www.ibm.com/cloud/watson-assistant/features/
and getting started instructions at https://cloud.ibm.com/docs/services/assistant?topic=assistant-getting-started#getting-started
If you opt for the plus or premium price plan then you can make use of search skill, which cribbed from the documentation -
When Watson Assistant doesn't have an explicit solution to a problem, it routes the user question to a search skill to find an answer from across your disparate sources of self-service content. The search skill interacts with the IBM Watson™ Discovery service to extract this information from a configured data collection.
If you already use the Discovery service, you can mine your existing data collections for source material that you can share with customers to address their questions.
However, you do not need to have a Discovery service instance. If you choose to create a search skill, a free instance of Discovery is provisioned for you. You can then create a collection from a data source and configure your search skill to search this collection to find answers to customer queries.
If you don't have a plus or premium plan then its still possible to craft in the Discovery search into your application using either your own orchestration or a cloud function.