Chestnut
I agree with strong, successful and confident but an alpha male doesn't necessarily need to be good looking, nor does he need to show a caring side, that is just a good quality to have.
What about Brian Blessed? He regularly used to beat his chest and dominate everyone! ?
An alpha male is a strong leader that others will either obey or respectfully listen to and defer to.
As Chestnut says, looks aren’t important and nor is a caring side ( in fact the caring side wouldn’t fit in with an alpha male.)
So, anyone in a really top position in society/ business/ sport would fit this term, otherwise they wouldn’t be in that position.
Alpha male, top dog or whatever you want to call it.
It’s not an insult or really a compliment either, although many do admire them.