Is saying, "If I succeed, I will pray two rak'ahs every day as thanks to Allah" considered a vow, even if there was no intention of making a vow or uttering it as such?

The statement made by someone, "I will pray two units (rak'ahs) every day as a sign of gratitude to Allah," is not considered a vow (nadhr (definition)) that must be fulfilled, unless you intended it as a vow. This is because a vow is made binding by any expression that indicates commitment, such as "It is Allah's due upon me." Therefore, nothing is binding upon you if you cease praying the aforementioned two rak'ahs daily, as long as you did not intend it as a vow.