The United States will not have the world’s biggest economy any more by 2050, but there is essentially no chance that it will fall out of any reasonable listing of “First World” countries by that time.
In order for the US to no longer be considered a First World country, one of two things would have to happen. First, the US could completely fall apart and our GDP could do something like being cut in half. That would get us to the lowest end of countries in the world that could be considered rich (but would still, if it were to happen today put us above many Eastern European countries like Poland, Russia, and Estonia). Second, there could be some huge wave of countries that grew so fast that they all got very far ahead of us. Then, we would fall out of the First World because we did not grow fast enough.
Neither of these seems even remotely possible. The US economy is weaker than it has been, but it is still relatively strong. A drop of 50% in GDP would be unthinkable because our economy is still essentially sound, even though we do have problems. The countries that are growing rapidly are still miles behind us in GDP per capita and it is not clear that they will ever catch up to us, let alone go far past us.
It is possible that we will not have the strongest economy in the world in 37 years. China’s economy, with their huge population, will be bigger than ours, if not stronger. But even if we are not the strongest economy in the world, there is no way that we will fall so far as to drop out of the “First World.”