What is called "reflexiv verwendete Verben" here are verbs that are normally transitive with an accusative object:
Anna langweilt den Barkeeper.
Ich beruhige den Hund.
With these verbs, using them reflexively is just a special case of their transitive usage. "Mich/dich/sich" is in that case really just the accusative of "ich/du/er/sie/es [selbst]".
Anna langweilt sich.
Ich beruhige mich.
"Real reflexive verbs", in contrast, only work with reflexive pronouns. There is no meaningful way to replace the reflexive pronoun by an accusative object.
That's all there is to it.
So what do we have to do to discern a "real reflexive verb" from a "fake" one? We have to check whether the reflexive pronoun (sich, mich, dich ...) can be replaced by a different accusative object. If it's "real", it can't.
If we know the verb well enough, for example as a native speaker or with a good understanding of German verbs, we can do that by using the "wen" recipe: We replace the preflexive pronoun by "wen", and then we check if we get a question that makes sense.
Anna langweilt sich. => Anna langweilt wen? => Question makes sense, she could e.g. den Barkeeper langweilen.
Ich beruhige mich. => Ich beruhige wen? => Question makes sense i could e.g. den Hund beruhigen.
Ich beeile mich. => Ich beeile wen? => Question makes no sense, one can only "sich beeilen".
In summary, if you know the word well, you can use the "wen" test to check if the verb is a "echtes reflexives Verb".
What could you do with this hard-earned knowledge? You could tell someone who doesn't know the verb as well as you that it is indeed an "echtes reflexives Verb", and they would know to never use it with an accusative object. It's terrific.