casual swagger of a charming billionaire = casual confidence of a charming billionaire

Hi! He is a billionaire. He is probably a confident, ambitious and proud person. Swagger is used to describe the confident way he walks around. It is usually disapproving. "Look at the swagger of that man!" "I know, he is so arrogant!" 'He casually swaggered into the room and told us all that his sales figures were much higher than hours'

Picture somebody walking along without a care in the world, relaxed, taking his time, and exuding an air of confidence. But, just a small point to think about Paweł - instead of saying "what means X ..." say "what does X mean".

relaxed, comfortable, confident. swagger can also refer to how a person walks, "holds themselves".