I'm trying to ask, "Are you sure you want to start a new game?" My best guess is, 你確定要开始新遊戲?
I'm not sure whether I used "start" correctly.
Your guess is correct. You can use it as the following examples:
start a new game - 开始新游戏
start to do something - 开始做某事
a good start - 一个好的开始
Other comments are good I just want to add if you are trying to stay "start" a "new round" of a game you are already playing you should probably say something like
重新来一盘 Or 重新来一次 or 重新来一回
Depending on the context...
You already know how to say "are you sure you want to" - so I won't bother commenting on that
Yes. Start——its original meaning is "do something from beginning". So “开始” is translated well.
you're right and but perhaps you should use the "restart the game ?" the best mean about your sentences : 你确定,你想开始新游戏吗?
你確定要 开始 新遊戲?would be good if you mean to play another game instead of the one you'd been playing.
你確定要 再玩一次? is better if you intend to start a new match in the game you'd been playing.