Unlimited Opportunity Attacks, but only one Reaction for the 5' movement.
Tunnel Fighter states (emphasis mine):
As a bonus action, you can enter a defensive stance that lasts until the start of your next turn. While in your defensive stance, you can make opportunity attacks without using your reaction, and you can use your reaction to make a melee attack against a creature that moves more than 5 feet while within your reach.
The main gist of this is that with Tunnel Figher, Opportunity Attacks no longer utilize your single Reaction and therefore you can take as many Opportunity Attacks as have been triggered.
In the case of an enemy "running circles around a character", the following would need to occur:
- Creature enters your reach
- Creature moves at least 5' (can expend your one reaction to make a melee attack against them). Note that this is NOT an Opportunity Attack, but simply the use of your single reaction.
- Creature moves out of your reach and triggers an Opportunity Attack
If the creature chooses to Rinse and Repeat (but why, man, why?!), then the cycle begins for 1 and 3 and skips Step 2 (you still only get one reaction.)
Unearthed Arcana isn't necessarily balanced
Having unlimited Opportunity Attacks may be unbalanced, and may be why they never made this official. Unearthed Arcana is playtest material, and this particular UA has been out for 3 years with no updates or official release. DM beware :)