And straight was a path of gold for him, (3)
The sun has a path of gold here, which seems to indicate that even nature experiences duty in the poem. Whether it's the sun or the mountains, everything has a purpose. The "gold" in this line also gives us a sense of reward that comes from fulfilling one's duty, whatever that may be.
And the need of a world of men for me. (4)
That phrase, "world of men," carries all sorts of connotations with it. But the main one here seems to involve the ideas of duty and responsibility that the speaker feels towards the outside world. After all, it can't be all about the inside world and those loving feelings he had the night before. Instead, we think the speaker's pointing towards a sense of balance between the inside and outside worlds, focusing mainly on the latter in this poem, of course.
Round the cape of a sudden came the sea,
And the sun looked over the mountain's rim: (1-2)
We've got it all here: sea, cape, sun, and the air. In just two lines, the speaker makes it clear that he's absorbing all of nature's landscape here. Nature, in turn, reflects his own motivations in the poem as the sun checks out the new day in the same way the speaker does.
And straight was a path of gold for him,
And the need of a world of men for me. (3-4)
The parallelism we see here really blends the speaker in with his natural surroundings. The sun has a path of gold set out before it while the speaker has his world of men. It's all connected here, which reminds us that everything has its own path and purpose to strive for.