Are humans still competing in the same way now that the first life forms did?
It's important to realise that evolutionatry competition and the common usage of the word competition do not mean quite the same thing. For example, you could talk about Usain Bolt competing in the 100m but this is only evolutionary competition with the other athletes in they are in competition in terms of evolutionary fitness. Evolutionary fitness encompasses ideas of survival, reproduction and the nurturing of offspring. The only thing that matters, from an evolutionary point of view, is how many successful offspring are produced1. Where human competition does not relate to this, it is not related to competition in the evolutionary sense.

People certainly do still compete in the evolutionary sense for mates, resources, etc. but in the West, in particular, much of human competition has become a very long way removed from anything that relates to evolutionary competition except in the most tangential of ways.

1 - my favoured definition for fitness is number of grandchildren.