Think of what will be any consequences should this get into the press. Whilst the person was playing poker, you do state that it was front desk staff playing poker in the lobby, with a guest.
Firstly, be completely sure they were in a situation that could be called a dereliction of duty - if their duty is to welcome guests and just "be there", they could easily claim they were.
Secondly, as a hotel, you should be welcoming to your guests (or should I say Paying Customers). This person is your face of the hotel at night, welcoming back drunks and getting stick from customers who have a problem. The person they were playing cards with probably thinks your hotel is great, and the staff are fantastic, and may have told all their friends about it. Free publicity that your hotel could not dream of buying!
If you take draconian action, this person could claim wrongful dismissal, or constructive dismissal. The press would pick this up, and see this as a story about a big bully hotel victimising an employee that was trying to be nice to a guest. Watch your bookings drop if this was to happen.
As someone said, provide e-learning, and other activities that can be done, so that the person is not sitting around with little to do; and perhaps have a quiet word about that some guests may see that as being inappropriate, and that a polite "sorry" should be given to the guest wanting a game. Bring in HR and you have am upset, disgruntled employee, especially if they think they were doing no harm.