I've played both but aside from getting to fight as different people in Chaos Bleeds the first Buffy game is better to play than the sorta sequel.
Yeah, that little guy is Sid the Dummy. Chaos Bleeds seems to be a fabled lost episode or something in which the The First alters reality and brings back some demons who've died, during the Buffy series, Adam and Kakistos and such. The story is obviously placed before season 7 and I'm guessing before season 6 as well but not sure.
The first game is set in season 3 but very awkwardly according to the lines mentioned in it. It seems to occur after the ep in which Spike returns and the enxt episode that followed, which makes little sense timewise as he had to go all the way to South America to get Druscilla. anyways, the story there seems to do with the ressurection of the Master, big bad of season 1.