It is a well known issue that many Android phones switch off the accelerometer when the screen goes off. However something seems to have changed with Android Fit (the app).
Every normal Thread is keep on working when the screen goes off or when the Activity lost its focus...but when the activity gets killed then all thread are killed...
However you can use services for longrunning tasks like asking the accelerometer for example
As Ilja said, your code runs even after the screen gets turned off. But in this case I guess we need a little different answer.
They definitely use a Service that keeps a wakelock and they query the sensors for data. Important part here is holding the wakelock - you have to prevent the device from going into sleep during lifetime of your service - if you don't want to miss some data.
But this approach will be drain the battery really fast, because in order to detect steps you need to process quite a lot of data from sensors.
Thats why there is sensor batching. That allows you to get continuous sensor data even without keeping the device awake. It basically stores the sensor events in a hw based queue right in the chip itself and only sends them to your app (service,..) at predefined intervals in batches. This allows you to do a 24/7 monitoring without draining the battery significantly. Please note that only supported chipsets can do that (you can find details in Android docs), in case of older phones you need to fallback to the hideous wakelock keeping method in order to get your data.
You can also just use Google Fit APIs, but this would only work when there're both Google Fit + Google Play Services installed on the device with monitoring turned on.