1) The game of backgammon (OED) but possibly used more widely for other board games.
These were being imported into Hull in the fifteenth century: 1453 2 duss’ par’ playng tabilles
60 scok tabylmen
1472 suffers me to play in his hous at the tables for mony, Selby
1490 De j pari tabellarum, York
1568 Item 3 pare of plaing tables with men for the same, Healaugh Park
1607-8 Richard Fawcett of New Malton for keeping unlawfull games or play at cardes and tables in his house. A Ripon inventory of 1485 has: tabula lusoria cum hominibus, possibly chessmen, and a Bury will of 1459 has unum par de tablis cum chesemen et tabilmenys. In 1619, 5s was Given to my lo[rd] to play at Tables in the Great Chamber of Skipton Castle.