I collect game dice as a hobby. What is a word for someone who collects dice?
If you mean what is the word that has the same relation to game dice collection as philately to stamp collection?
Then, I don't think there is already one (also note: while dictionaries define philately as collection and study of stamps, according to encyclopedias stamp collecting is not the same as philately, which is the study of stamps, see here and here).
If you want to be inventive you could attempt to coin:
phil- "loving" + astragaloi "knucklebones"
EDIT: This form was chosen due to etymology of philately
The word "philately" is the English version of the French word "philatélie", coined by Georges Herpin in 1864. Herpin stated that stamps had been collected and studied for the previous six or seven years and a better name was required for the new hobby than timbromanie, which was disliked. He took the Greek root word phil or philo, meaning an attraction or affinity for something, and ateleia, meaning "exempt from duties and taxes" to form "philatelie". The introduction of postage stamps meant that the receipt of letters was now free of charge, whereas before stamps it was normal for postal charges to be paid by the recipient of a letter.
The alternative terms "timbromania", "timbrophily" and "timbrology" gradually fell out of use as philately gained acceptance during the 1860s.