It isn't an extra game, but rather down to the competition. It is since the Checkatrade trophy allows under 21 teams from PL and FL teams. A sent off player, or one who reaches caution thresholds, is suspended until his team has played x number of 1st team games, non-first team games don't count. If they allowed Checkatrade games to count, you could have a situation where, let's say for arguments sake, Gary Cahill is sent off for Chelsea in a Premier League game. Chelsea could argue that he would have played in that Checkatrade game and that as a result that should count as one of his suspension games, which is clearly a nonsense.
Unfortunately this disadvantages the lower league teams who don't have a reserve team in the competition, as for them the Checkatrade Trophy is a first team game but that first team game doesn't count towards the suspension. The more sensible approach would have been to say that it doesn't count for suspension serving purposes for teams that have a reserve team in the competition, but it does for those that have their 1st team in it.