"남자가 바다로 달립니다."
Translation:The man runs to the sea.
"영어로 말합니다." doesn't mean that you speak according to the rules.
And "in the direction of" means towards it. I'm guessing you mean "according to" as implying that the person is running bedside on the beach following the ocean shore? If so, that's not what "바다로 달립니다" usually implies.
According to someone on this forum (https://www.italki.com/question/317170?hl=ko):
달리다 and 뛰다 are nearly the same when they mean "run".
They have different usage when applied more widely. 달리는 기차(O), 뛰는 기차(X) -> 달리다 can be applied to vehicles, 뛰다 can't. 뛰는 물가(O), 달리는 물가(X) -> 뛰다 means "jump" as well, 달리다 does not.
로 is talking about "to" or in context "I am going to the beach". 에서 is referring to more about where you are like "바다에서 수영했어요" (although I believe the more proper form is "바다에" in that sentence). 까지 is talking about "up to" such as in "나는 여기 까지" which can mean a multitude of things that which you are implying.
로/으로 deals with a location. 러 deals with an action; modifies a verb.
Sometimes Duolongo causes confusion when there is no need. While Google Translate is certainly not the definite expert of meanings of words, it does clarify the general meaning. 바다로 and 바다으로 are both defines as by the sea not "to" or "toward". Therefore, the man runs by the sea is the general meaning. 바다 throughout this tree is variously defined as sea and ocean and therefore either should be accepted. Teach us the basic language before adding these "sometimes" or "obscure" meanings.
In the context here, 로/으로 means towards (in the direction of). "남자가 바다로 달립니다." means "The man runs towards the sea/ocean."
Although, in other contexts it means "using" or "by way of".
Ex: "I ride to work by bus." -> 저는 버스로 일에 타요.
"We talk together in Korean." -> 우리가 같이 한국어로 대화해요.