There are literally 5 members in BRICS: Brazil, Russia, India, China and South Africa. South Africa is not participating. So, instead of using BRICS, it would be better if we are honest and say "Why are Brazil, India and China participating?" Also, it would help us in asking the same question to other countries participating like Argentina, Mexico, Thailand and NATO member Turkey.
But once we do that, we might realize that participation in these games mean nothing. Majority of the nations don't even care for the official Univerity Games, let alone Russian version of University games. Russian authorities would have approached some Universities from these countries and invited them. These universities sees it as a good opportunity to brag that their athletes represented the nations and won medals at an international event. Russia gets to brag that they got so much participation. And media gets to scare monger NATO vs BRICS/SCO like Allies vs Axis. And I find it really hilarious because except some China shrills, BRICS is considered a dead option in India. Majority of security establishment considers China as an enemy and Quad as future. And regarding Indian pariticpation in SCO, the running joke is that just as Pak was in SAARC to ensure nothing gets done there, India is in SCO to ensure nothing gets done.