***** NOT A TEACHER *****
Hello, Captain:
If I understand your basic question, you want to understand the difference of meaning of the word "always" (or similar adverbs) when it is used in the present tense and when it is used in the present progressive.
I have found some information that may interest you.
1. "They always play chess."
a. This sentence needs more context.
i. For example: "They always play chess on Friday evenings."
(a) It means "on all occasions."
[Only my opinion: I guess that means something like: "No, they won't be free next Friday evening. They always play chess on Friday evenings."]
2. "They are always playing chess."
a. This sentence does not need more context.
b. It implies that "at any time [that] you care to mention they will be engaged in playing chess."
c. Of course, this is "hyberbole" or overstatement. [Only my opinion: That sentence is absurd, for no one can spend 24 hours a day playing chess!]
d. Because of the hyberbole, the speaker is probably voicing some disapproval of their behavior.
Authority: Rodney Huddleston, Introduction to the Grammar of English (1984), page 156.
*****
3. "The adverbs always (in the sense of 'frequently') [my emphasis], constantly, continually, forever, perpetually and repeatedly can be used with progressive forms to describe continually-repeated actions." [my emphasis]
a. "She's always helping people." [Only my opinion: As you can see, this "always" is very different from the "always" in "The sun always rises in the east."] [Only my opinion: "She's always helping people" seems similar to "As always, Mr. Smith is being overly generous." That could be a compliment or even a bit of criticism, I think.]
Authority: L.G. Alexander, Longman English Grammar (1988), page 165.
Credit for the "sun" sentence goes to Otto Jespersen in his Essentials of English Grammar (1933), page 266.