There are no romantic feelings between the two, but they do care about each other. This is a bromance that is as close to BL as possible.
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In that case, please remove "BL" and "Yaoi" tags. It's misleading for users. BL = romance. No romance = no BL. "Friendship" tag would fit better. You wouldn't call a game with female protagonist yet zero romance with male characters an "Otome", right?
"Bromance" is a term often used to discredit shipping between two male characters by homophobes, you should probably stop using that term in general.