I was just wondering why this isn't part of the sports stack exchange site.
Stack Exchange sites are defined by their community. If the community of chess enthusiasts is sufficiently active and sufficiently distinct from any other site's community, a separate site may be warranted.
Yes, Chess can be classified under sports, but it is quite different from the sports that are discussed on Sports Stack Exchange, which is essentially about competitive physical activities.
Chess is more naturally classified as a board game. A stronger case could be made for it being a part of Board and Card Games. But historically, Chess and Poker developed into separate sites, while Board and Card Games became dominated by fantasy card games. Again, it's mostly about people. It might be more efficient for my family to be merged with my neighbor's, but this is unlikely to happen.