It is not necessary to be Unbeatable to be Overpowered.

Imagine the simple game Rock, Paper, Scissors. Imma modify the game slightly to be Rock, Paper, Scissors, Eagle. Eagle beats Paper AND Scissors, but is beaten by Rock.

Within this game, Eagle is not Unbeatable. You beat Eagle by throwing Rock. However, it *is* Overpowered. Suddenly, in a game built around everything having equal odds, there is now something with a higher % chance to win than everything around it. Now, because it is not Unbeatable, the game hasn't necessarily become "Throw Eagle every time or lose." The problem is that the game suddenly revolves around the Eagle. You would either be playing Eagle, trying to counter your opponent who you think will play Eagle, or trying to counter your opponent who you think will try to counter Eagle. 
With the new ruleset, where the whole game revolves around Eagle, you have effectively removed Scissors from the game. All they are good for is beating Paper, but Eagle also beats Paper so why the fuck would you use Scissors?

In this game, Eagle is not Unbeatable but is Overpowered. It is Overpowered because it is Very Strong.

You can be Very Strong and not be Overpowered, though. Most competitive video games have magnitudes more complexity than Rock, Paper, Scissors. One character/ability/whateverthefuck can be made to be more powerful than most things in the game *without* having such an outrageous effect as Eagle did. Unfortunately, the nature of "Very Strong vs. Overpowered" relies on these complexities, so it is not as easy to create such a clear example from scratch.

I'm going to do my best to use an existing example from the only competitive game that I know all that well (SSBM) to try to make my point but it may not work so well....

Peach's Down-smash is what I'm going to stick with. It is almost impossible to argue that Peach's Down-smash is not Very Strong. It has very low delay between input -> damage box. It can be used to end combos and it can be used to try to space people out. It does big knockback at high% and can be used to kill. At low% it can be used to build up a whole lot of %. If DI'd unfortunately it can land a whole lot of hits and do ridiculous amounts of damage. Essentially it has a large variety of uses and is a very important part of Peach's arsenal.

At the same time, I would argue that you can't really call Peach's Down-smash Overpowered. If you throw the attack and it doesn't connect, it doesn't leave you protected from above. The whole cast has pretty strong options from above, so this is a definite weakness. It takes >1 frame for the attack to have damage boxes so it ain't no Shine. Peach is a character that has a few staple moves (turnip, nair, dsmash, grab shenanigans), but really relies on a *lot* of her moveset to succeed, so you cannot use the argument that Peach is a high tier character because of Down-smash alone. In a vacuum, her Down-smash is not all that breathtaking. It is Very Strong, and when you put it in a vacuum and compare it to the vast majority of moves in the game, it's really really dang good. It's hardly Overpowered, though. It has counters, it has weaknesses, and it relies on support from the rest of Peach's options. It doesn't have matchups that entirely revolve around it. It's game-changing without being game-defining.

In closing - I feel that Overpowered is very reliant on the context of the game that contains the Overpowered thing. To be Overpowered, you do not need to be unbeatable, but you need to be much more than simply Very Strong. You need to be so strong that you actually change the entire game. Most every choice made in the game would have to be made based around an Overpowered aspect. As with Eagle, where even when neither opponent chooses Eagle, their decisions of what to throw have been made entirely *because* of Eagle - the Overpowered aspect remotely dictates decisions made, even in the Overpowered aspect's absence. Maybe a character that isn't very strong in a vacuum (like paper) becomes more viable and pickable just because it has a slightly better chance against the Overpowered thing.

Being Overpowered is being so strong, relative to the rest of the things, that the whole game necessarily (and sometimes indirectly) revolves around you.