Will most jobs that are done by humans at some point in the future only be done by the smartest humans in the world?

The smartest humans are the ones that don't have to work.

In much less than 1000 years, there be machines that manage and program robots, so we won't need humans for that either.

What makes you think 1,000 years from now we won’t be in another dark age, due to our in ability to deal with running out of oil, series of climate problems, nuclear radiation poisoning, or other catastrophe? Progress is no linear or exponentially pointed in one direction. We are just as likely to be in a place similar to where we were 1,000 ago then further along from where we are now. 

However, if I am going to subscribe to your vision of the future. Robots become self-replicating, self-repairable, self-programmable, as humans try to find ways to get them to do and solve problems we cannot. They then realize we are not needed, are a drain on resources and are eliminated. Should we somehow manage to make our robots not become self aware, which the way that unfettered Silicon Valley programming, AI development, and app creating makes it clear we will not be able to stop. This will be the outcome.

Also if your described future is the true future, who says programming is going to be some sort of advanced skill? Even today with a template anyone can create a website with Square Space or other website builder system. It will likely be that robotics will be similarly accessible to the masses. 

However, taking this future at face value. The jobs, or places people will spend their time/effort if basic needs are met, will likely be in artistic, athletic, or other self-improvement tasks. Possibly even in the psychology/psychiatry fields as people will likely have existential crises about why they should live.

I don't think so... no

As long as people remain to be Humans.. Humans in relationship with themselves and those around them, as long as they see each other as great potentials and not just resources for profit.

Qualities such as kindness, honesty, empathy, sincerity, holding on to the most basic values, morals and standards such as family, being faithful and loyal, understanding and accepting true nature of creation... those are the people who's "job" is irreplaceable no matter what iq they have because they are born to feel and enjoy life, and their desire to live is much greater than those who don't feel life.