I am the author of the statement. Does the power to decide which context he or she chooses to use not within the author?
Not really. Authorial intent is one of many legitimate interpretations of text. To assert your authorial interpretation as the correct one, to back up your "claim" you need to back up and provide reasons why your context is the correct one to use. By what grounds? What criteria? And why should we believe those criteria are good criteria? Just because you assert that in your narrow authorial context, your statement is true doesn't mean it is the legitimate one. Hitler asserted that mass genocide of Jews was correct and good, since he was the "author" of this does this mean his ideology is right? By most measures, the answer would be no.
A group of beliefs make up a system of beliefs, which make up religions and religions make someone religious.
The proposed questions is, do all systems of beliefs make up religions?
My answer is, are all systems of beliefs used to guide a persons life? YES, tell me one that doesn't.
Just because you say something is an answer doesn't make it so. I could say 1+1=5 but that doesn't make it true. The burden of proof is on YOU to show that all systems of beliefs are necessarily a religion, as you were the one who are arguing that something is true. It is your job to show us that something is true, not for us to show you it is not.
Also note that your definition specifies a "system of beliefs" meaning that taken literally, as you so often like to do, it means the a single belief does not compose a system. Suppose for instance a person has a belief that trees are plants does this single belief make it a system? No. Suppose that the same person also has another belief say that dogs are animals. Do these two "beliefs" necessarily make up system? If you can prove that, again, it YOUR JOB to show that this is true, that 2 or more unrelated beliefs make up a "system."
One more thing you're doing here, you're establishing an equivalency between the word "group" and the word "system." Although in certain contexts, they can be used interchangeably, is this necessarily the case in this one? Why? How so? Just because you say so? That's not a valid reason to adopt your particular definition of "group" over another. Just because it can be defined in such a way doesn't mean it has to be. Like you stated with your "running" example. You need to detail precisely why your definition is the best one, not just authoritatively assert it. By that logic I could just as easily assert that 1+1=5 and it would be legitimate. You need to provide actual REASONS.
Also, try science. I would argue that science in its purest form is not a system of beliefs, but rather a system of methods and procedures designed to approximate a means to measure objective reality. Science doesn't "believe" anything. Everything in science considered "fact" is subject to change in the future (except, math, assuming the math is correct) when new discoveries are made. Science doesn't require belief, it provides empirical or theoretical reasons why something should be accepted as true.
Something else to consider: Suppose we create a computer program that can be considered "sentient" does that mean that this artificial intelligence is religious? If so, why or why not?