The meaning of "Have been around"

In the following context (excerpt from this answer):

They're examples of the double genitive/possessive, which is perfectly valid and has been around in English for centuries. The "of" already denotes "possession", but we do this again when we use mine/his instead of me/him.

I think has been around means exists in this context, but I can't confirm it. I tried to look it up in the dictionaries, but with no luck except as follows: From Wiktionary, have been around the block is an alternative form of verb phrase to have been around, which idiomatically means "To be experienced in worldly matters; to be seasoned, not naive." From Longman Dictionary of Contemporary English, the 13th entry for around (have been around, informal) is

a) to have had experience of many different situations so that you can deal with new situations confidently : [eg] You could tell this guy had been around a bit by the knowing way he talked.
b) to have had many sexual experiences – used humorously

Can anyone help me to confirm that has been around means exists in the context I quoted?

Yes, has been around means 'has been in existence'. The OED gives only ‘to have gained much experience in the world’ but in practice the expression is used rather more widely, if only in informal contexts.

The use of "around" as an adverb meaning literally "in one's present location" and metaphorically "in one's present situation" is attested in Merriam-Webster:

around adv \ə-ˈrau̇nd\ 2 c : in or near one's present place or situation <wait around awhile>

Thus your example sentence:

[The double genitive/possessive] is perfectly valid and has been around in English for centuries.

should be understood to mean:

[The double genitive/possessive] is perfectly valid and has been in its present place or situation in English for centuries.

The reason why around means "in or near one's present place or situation" (thanks, MetaEd) is because it's really a round. I.e, a circle is involved, centered on the object of around. If around is intransitive, as it is here (i.e, it has no object), then its object is assumed to be the speaker. So around by itself means around me or around here.

This is what around means:

Stand up, look straight ahead, turn to the left or right and keep looking straight ahead; continue turning in the same direction, observing what's in front of you, until you have returned to your starting point. You have turned a round, or around, and everything you have seen is what's around you, or just what's around.

Dictionary definitions frequently don't distinguish the basic meanings from specific usages and extensions of terms.