-리 is a literary sentence ending similar in meaning to -ㄹ 것이다 or -ㄹ 거야. It conveys a mixture of one's intention and future prediction. It is too literary for use in speech, but quite common in song lyrics and in writing. It gives a feeling of a resolve, hope, and wishful belief. There is also a longer form -리라, which is also common. For example, - 오늘을 잊지 않으리(라) = I won't forget today. - 이 모든 게 헛되지는 않으리(라) = (I know/believe) All this won't go to waste. So 빛나리 is like "They/it will shine" or "They shall shine".

yes, i know 빛나다 is to shine, but does ~리 add anything to the meaning?

Im pretty sure it means shine