You could try iterating through the games array and removing any that match the current game.
Untested code:
//...
var upcoming_games = Games.find({hype: {$lte: current_game_hype}}, {sort: {hype: -1, submitted: 1}, limit: 10}).fetch();
var upcoming_games_modified = upcoming_games;
upcoming_games.forEach(function(game, index) {
if(game._id === current_game_id)
upcoming_games = upcoming_games_modified.splice(index);
});
return upcoming_games[skip + 1]._id;