Let me repeat: a person who works on their own without petitioning deities for help has a non-theist practice, regardless of whether they are theist, atheist, apatheist, ignostic, agnostic, transtheist, or anything else. This is a case where a person who has an exclusively non-theist practice may be a theist in belief, or atheist, deist, apatheist, ignostic, agnostic, transtheist, or anything other god-or-non-god-related belief.
Anyone can engage in non-theist practices, such as mindfulness meditation, jhana practice, breath-directed meditation, mudra practice, etc. Their beliefs are not relevant to their non-theist practices. I happen to be a transtheist who engages in non-theist practice. My beliefs may go back and forth between atheism, theism, polytheism, pantheism, agnosticism, ignosticism, or whatever. My beliefs don't matter. Beliefs come and go. It is the non-theistic practices that matter and produce the lasting effects.
This is a major difference between non-theism and atheism.