perhaps answered in the past, in which case i apologize;

but do players have, or can achieve, rights to the games they played.

such as, am i breaking any laws/ is it copywrite infringement if i publish a game that was played by someone else without due credit?

games are not owned. collections of games CAN be. law isn't totally clear. you are fine :)

Could a secretive individual hide his or her games archive to others, while still retaining the ability to access it?  Current games?

The moves themselves cannot be copyrighted.  The annotations can and generally are copyrighted.  It would be difficult, IMHO, to copyright a collection of games unless there was something unusual, special, individual about the collection, since each game itself isn't, but I'm not sure how that would work.

Publishing a game without noting the players is not unusual.  It is also not uncommon but not unheard of for the same game to be played by different players, i. e.   A&B play a game which duplicates, move for move a game played earlier by D&C.