Hello!
Here 라 is a short form of 라고.
(이)라고 생각하다 means "to think that someone/something is + NOUN"
운명적인 상대라(고) 생각했다.
I/He/She thought that he/she was a fateful rival.
Quoted from
http://talktomeinkorean.com/lessons/level-5-lesson-10/
-(이)라고 is usually not used alone but used with words that are related to speaking, such as 말하다 (to speak), 이야기하다 (to talk), 대답하다 (to answer) and also with 하다, which in this case means “to say”.
-(이)라고 말하다 = to say that it is + NOUN
-(이)라고 대답하다 = to answer that it is + NOUN
As you can see above, -(이)라고 is used with nouns and is a way to quote the words before -(이)라고 and take the
meaning of “(say) that S + be”
Construction
Nouns ending with a last consonant + -이라고
Nouns ending with a vowel + -라고
Ex)
하늘 (sky) + 이라고 = 하늘이라고
나무 (tree) + 라고 = 나무라고
Meaning
하늘이라고 = that it is sky, “sky”
이거라고 = that it is this, “this”
Used with other words
-(이)라고 is usually used with words like 말하다, 이야기하다, 대답하다, etc and when used with -(이)라고, the verb 하다, which originally means “to do” takes the meaning of “to say”.