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Johnny the Magnificent died to a monster in a dungeon wearing a ring of mind shielding. His soul entered the ring and there he lived for centuries. Now Jack the Rookie picked up the ring.

What can Johnny do from inside the ring besides talking to Jack or departing to the afterlife? Is it considered an intelligent item?

Johnny can only do exactly what the description says he can do. Which is communicate telepathically with any creature wearing the ring or depart for the afterlife.

On your question about whether its an intelligent item: It is not quite the same as the 'sentient items' described in the DMG as it is the soul within the ring that is intelligent rather than the item itself, though many sentient items blur this line since their power often comes from a soul trapped within it.

It's the subtle difference between an existing magic item that just happens to contain a soul, and an item (typically unique) that either gained sentience by virtue of a powerful enchantment or gained it's actual power because it trapped a soul.

However, the question is moot (unless you have a situation that proves otherwise), since the soul in this case can't do anything other than what is described and doesn't have any other power over the wearer so there is no need to provide other stats etc.

Johnny can only do what the description says. He can communicate telepathically or depart for the afterlife.

In a few cases, communication is sufficient to do things. I mean, you could teach Jack about an ancient earbug song. Or you could mislead Jack into entering a Lich's trap in exchange for the Lich helping you get a body.

There is even the UA Diplomat feat that grants you the ability to charm someone by talking to them; telepathic communication would count as talking in any reasonable sense. Charming doesn't do much here, other than grant you advantage of further social skill checks and make Jack unable to harm you (charm in 5e isn't charm from 3e, it is highly limited). Similarly, you could perform a song using Performer and distract Jack with a disadvantage on Insight and Perception checks.

If worn by an animal, the Animal Handler feat (from the same UA) would let you command the beast. Your inability to see what is going on makes this less than useful, however.

Johnny has no ability to cast spells, no ability to maintain concentration or do actions (the Diplomat ability isn't an action, however). Anything that isn't an action and can be done by talking or communicating with someone can by done by Johnny, and only on Jack.