If you 'get to do' something you have the opportunity to achieve an ambition or to do something enjoyable or desirable.
If you 'got to do' (more correctly 'have got to do' something) this means that you are obliged to do something.
My understanding of the phrase is this:
Eric Thomas is a motivational speaker, and I presume that 'I get to, not I got to' is one of the ideals that he wants his listeners to aspire to. It may refer to being a successful and independent person, in business and in life.
Successful people get to do what they want to do, rather than what other people tell them they've got to do.