The deities on these chess are Chandeeswara, Nandi, Garuda, Hanuman and Chandeeswara. These are modern, from the twentieth century, and are well made. The pieces are cast individually and the patterns are chiseled on them. See the slight difference in the patterns on the Chandeeswara.
The actual functions in chess can only be assumed, except for Chandeeswara. It is quite likely Chandeeswara is Pawn, the number and the relative size are the indicators.
The quality of workmanship is well above average. See the Garuda for the number of patterns, delineation of fingers and toes, the wings (rear view) and the lines on his sole.
While the quality of workmanship is noted, it is unsettling to see my deities being given a different and non-religious role.
Hope the rest of the pieces find homes where they are treated with respect. The tallest of these, Hanuman, is about 6.2 cm in height.
It is quite likely I will revisit this topic after I reread the book Lives of Indian Images by Richard H Davis. Highly recommended reading.