Yes, it could; and the word was once used in that way. Actually you still can exercise religiously, clean religiously. An older meaning for 'Religion' is 'repeatedly' or 'with regularity'.
Words evolve and change over time. Words can also be used in a variety of creative ways, through figures of speech, etc. Religiously cleaning and religiously exercising are figures of speech, not religions.
Yes, the label ‘religion’ has been inherited from other uses. The label is not what is important. What is important is that we see a variety of belief sets that seem to share certain characteristics. What are the characteristics that are shared, if any. I would argue that my definition presents characteristics that are shared by belief sets that are considered a religion.
When defining a religion you don't have to explain why people do things. You only need a tag, and really that is all you can hope for. Christians do such & such, and they commit to believe and such. You don't have to explain why just to identify what religion they are in.
A tag or label requires a meaning to be associated with it, otherwise it is simply a meaningless group of symbols.
Zen is one. Another one might be a warrior religion where the goal is to die honorably and achieve glory in death. You could also have a community religion where you commit to your community. The masons come to mind.
When you say Zen, do you mean the physical practices disassociated from Buddhism or are you referring to Zen Buddhism? If you are simply referring to Zen practice devoid of any belief about the cause, nature, and purpose of the cosmos, then it would not be a religion, by definition. Perhaps it would be considered a Health and Wellness practice.
As for the warrior religion, if the goals you describe are part of a set of beliefs that include explanations for the cause, nature, and purpose of the cosmos, say in Norse Mythology, then it would be a religion. If the goals are not associated with any of that, then it would not be a religion, it would be better described as a warrior code or warrior ethos.
And last, I would in no way consider the Mason’s or the Rotarian Club to be a religion. I cannot see any consensus for the idea that commitment can be the sole criteria by which to define religion.