I see that the suffix of the league key is the league ID, is there anywhere where the prefix for the game type is defined? i see from examples, baseball 2010 is 238.
i'm not sure if i completely follow your question, but if you know the game key (the '238' value in your example) you can use the fantasysports.games table to get the 'display name'. thus: select * from fantasysports.games where game_key ='238'
brings you back info about that game, including the 'name' and 'season' values. unfortunately you cannot go the other way as you must provide either game_key or user_id in order to query that table.