The working genes they insert are just into the cell envelope itself, not into the cell nucleus. There are actually a lot of DNA that is free floating around in the cell, and are used during protein synthesis, called episome or non-integrated DNA. This is distinct from the DNA inside the nucleus, which gets copied from generation to generation.

There are techniques that work on modifying nuclear DNA but from my understanding it's much harder (like using CRISPR) and has a lot more risks for things like causing cancer due to off-site editing.

The scales that this technology works is mind-boggling. 10^12 to 10^14 per kg of body weight of individual viral particles that all must do the same thing, and work correctly at scale. Even a few errors could cause serious problems.