Good news! We’re currently rolling out drag and drop for messages and conversations into groups in Outlook on the web first for First Release customers, then Standard release customers.
It’s much easier to explain with a GIF:
Support for Outlook 2016 for Windows is coming soon–stay tuned.
You can find the documentation here: https://support.office.com/en-us/article/24e809db-70e1-45b7-8d54-efac7951dc95