This is not so simple as it seems. And I'm sorry to see you accepting a shallow answer.
First, orthopraxy does not mean disbelieving in God. It means that people align with or observe proper actions rather than beliefs. It appears that after prolonged confrontations with the early Christians, that based their religion on pure beliefs and dismissed rites, Rabbis chose the path of actions, developing practical Mishnah and Talmud that focus on details of everyday rituals rather than additional interpretational Midrashim. As it says (Pirkei_Avot.1.17): "וְלֹא הַמִּדְרָשׁ הוּא הָעִקָּר, אֶלָּא הַמַּעֲשֶׂה." "Study is not the most important thing, but actions;", and there are many similar sayings about the utmost importance of the actions.
I would agree with "the Times of Israel that in Judaism we derive beliefs from actions, not the other way around. A person that keeps Shabbos is testifying his belief in seven-days Creation, a person that davens is testifying that God controls the happenings, a person that keeps Seder Pesah testifies of the Exodus, etc.
Here's a test, I light a lighter on Shabbos in my shul just for fun. The reaction? I'm finished. But if I say out loud in the middle of a prayer that I don't believe in God, people will chuckle and think I'm going through hard times, maybe advise me to seek Rabbinic help.
Your example is different because a person openly asserts the insincerity of his actions which basically invalidates them and makes him technically totally secular. But had we not known his true intentions and only hear him denying God's existence, we'd judge by his actions rather than his words.
There's a reason that Halachicly a Jew is strictly required to prove his beliefs in actions, so putting Teffilin and reading Shemah out loud are mandatory while reciting the 13 Principles is not.