Shelter (the service that a house provides) is included as a consumption item in the CPI figures (and, as any adult would expect, has the largest weight of any of the 211 items that constitute the CPI basket).
You can see the significant changes to the calculation methods detailed here: https://www.bls.gov/cpi/research-series/r-cpi-u-rs-changes.h... The rent equivalent method for owned property has been in use since 1983. (Prior to that, housing was included in CPI, just with a different method.)