I visited the Pamplin Park museum near Petersburg a couple years ago (I recommend it to anyone who hasn't been there). Part of the museum is a recreation of a Civil War camp site, with a couple people portraying Confederate soldiers to describe camp life.
They did show us a couple of games. One I remember was called "Chuck-o'-luck." They had a hand-carved die and a little flat piece of wood rudely divided into six sections. A player would be allowed to pick two numbers before rolling the die. He would place markers on those two sections of the piece of wood and then roll the die. If one of his numbers came up, he won two of whatever they were playing for; if neither of his numbers came up, he lost one. The odds were such that, over the long run, the player could expect to break even, but a hot or cold streak could put the player well ahead or well behind.
That was the sort of game they showed us - very rudimentary, using handmade gaming pieces that could be fashioned after they got to camp. If they had chess sets or checkerboards, they didn't tell us about them.
My guess is that probably many of the soldiers knew how to play the games you mentioned, but probably very few common soldiers actually had them on hand. Such gaming implements would have been too much of an encumbrance for soldiers on the move.