Why is the result complement wrong?
Use 到 as the result complement of 猜 is not wrong

猜 = to guess

猜到 = to guess successfully/ correctly  

The goal of the game is to successfully guess the names of the dish. (not just making guesses)

Neither 的 in "[黄蓉煮的][美食的名字]"  can be omitted 


黄蓉煮的 is the adjective phrase for 美食
黄蓉煮的美食的 is the adjective phrase for 名字


"[黄蓉煮美食][的名字]" or "[黄蓉煮的美食][名字]" are both incomplete

Edit:

After seeing the picture, I think your teacher's correction was very sloppy.


If you wrote "遊戲的(内容)是猜(到)黄蓉煮的美食的名字", then 到 would be a mistake, you should write "遊戲的(内容)是(去)猜黄蓉煮的美食的名字 
"目的 (the goal)" is "猜到" (to guess right)" ; "内容/玩法 (the way to play)" is "去猜 (to guess)"


'目标' (the goal of winning) would be better than '目的' 

'去猜出' (figure out) would be better than '猜到'

(遊戲的目标是去猜出)


得 in 闻得出来了 is not wrong. Actually, the final particle 了 should be omitted because the sentence doesn't end there. 
Also he didn't correct 名子 back to, 名字 or 蓉儿 back to 黄蓉 


蓉儿 is a nickname only her loved one could use to address her. For us readers, she is always 黄蓉