As previously mentioned, it is because the verb interesar is similar to gustar in the way it is formed. So it is 'playing sports interests us' rather than 'we are interested in playing sports'. The us is in the nos, rather than the we=nosotros in a standard verb formation.
For french/spanish speakers: does "pratiquer des sports" (fr) mean the same as "practicar deportes" (es)? Is the usage and meaning the same? I personally wouldn't translate "pratiquer" as literally and only meaning "practicing" from French to English as its usages are slightly different, so I wondered if Spanish follows the same rules.