The actual date on the stele is almost certainly the Long Count date of 9.14.0.0.0 (assuming the researchers and the Smithsonian are using the same calibration dates, which seems likely since the beginning of a new katun would be an auspicious time to erect a new stele).

• 9. This is the Baktun, a period of about 394 years.
• 14. This is the Katun, a period of 20 years.
• 0. The first zero here is the Tun, the year less five days.
• 0. The second zero is the Uinal. Unlike all the other time periods on the list that count from 0-19, the Uinal only counts from 0-17.
• 0. the third and final zero is the K'in, one day.

Since the Long Count is a chronometer ticking slowly into the future day by day, it's a relatively simple matter of converting dates from one calendar to another. Not perfect, of course, because there is some disagreement over references points used to calibrate the Long Count against the Gregorian calendar. Hopefully a Mesoamerican specialists can discuss the nuances of those disagreements.

Also, maybe they answer a question that has perplexed me for a while: were the Wayeb, the five missing days leftover by only having a 360-day year counted by Long Count, or does the Long Count stop ticking for five days to resume once the Wayeb is finished?

The linked article says the following:

According to preliminary reading by epigrapher Octavio Esparza Olguin from the National Autonomous University of Mexico, one of the stelae was engraved on November 29, A.D. 711 by a "lord of 4 k'atuns (20-year periods).

Based on that, I assume that the epigrapher transliterated the date from the Mayan format to the format that we commonly use today.

The Maya had a very accurate calendar, as a matter of fact, but they certainly didn't use BC and AD! While they would have written the date in their own terms, we can follow their calendar backwards from post-contact times (where their calendar and the Gregorian one clearly agree) and thus get a date in our terminology to correspond with what they recorded in theirs.