how do you call a person who doesn't share responsibility

I'd suggest Poor delegator or anti-delegator or perhaps simply control-freak.

There's an article here about the phenomenon including this:

She was convinced nobody else in the company could do it exactly right — so she just did it herself. She could do it better anyway, she thought.

Sound familiar? Then you might be an anti-delegator. Even if you aren’t, you likely know someone who is. (...) Being a poor delegator can also affect you mentally, demotivate your team and hold up work for everyone else, said Lunsford.

A control freak is more informal and the most negative. From Dictionary:

a person having a strong need for control over people or situations.

In sports this person would be a ball hog. Someone who doesn't pass to other players because they want the glory for themselves or believe they're the most talented.

Overall, not a team player.

The analogy would be immediately recognizable in other contexts.

See also glory hog and show-off. Neither of them is a great fit, but carry many of the same characteristics.