It is just an attack, not ranged, not melee, not a weapon, not spell
Let's start with the obvious, the item doesn't say it's melee/ranged/weapon/spell.
The ring isn't a weapon, and although it is magic it isn't creating a spell.
The ring hits at 60ft, so it's not melee.
The attack can hit a target 60ft away, so maybe it is ranged?
Ruling that it is ranged has consequences
We need to think carefully about whether or not the attack should be classified as ranged, because that ruling has consequences. If we say it is ranged then when it hits a target 5ft away you will be rolling at disadvantage. There are other interactions with ranged attacks (eg Arrow-Catching Shield) which you are imposing on the ring with this ruling.
The rules do not include a description of how to classify attacks as "ranged attacks"
While the ring does seem similar to a ranged attack, we should try not to bend the rules to our ruling. Rules do not exist to be rules lawyered into a conclusion that we are trying to confirm, we should instead read the rules to discover what the correct conclusion is. The rules say:
When you make a ranged attack, you fire a bow or a crossbow, hurl a handaxe, or otherwise send projectiles to strike a foe at a distance.
They do not say:
When you fire a bow or a crossbow, hurl a handaxe, or otherwise send projectiles to strike a foe at a distance, you make a ranged attack.
We should be careful to not think these are equal. The first is not a definition of can be classified as a ranged attack, it is a description of what things we already know are ranged attack are.
The rules go on to say:
You can make ranged attacks only against targets within a specified range.
Attacks made against targets within a specified range are ranged attacks.
Is there even a projectile?
Even if we do incorrectly interpret this rule as "anything that sends a projectile to strike a foe at a distance is a ranged attack", then in this case what is the projectile?
The ring says it "a spectral ram's head", to me that sounds like the ram's head appears, it doesn't seem to imply that the ram's head is shooting from the ring at the target. In my mind, the ram's head appears by the target and hits them.
Ring of the Ram is an attack at up to 60ft
We can conclusively say that Ring of the Ram does not make weapon or spell attacks. It is also not listed as a melee or ranged attack, so we can conclude it is neither of them either. It's just an attack at up to 60ft, that's all.