What are the minimum conditions required for "open-ended evolution"?
In principle open-ended evolution can occur with condition one violated. Because evolution is simply a change from one generation to the next (see answers here, here, and here), the is no requisite for a "non-trivial minimal criterion". Such a minimal criterion (e.g. survival to sexual maturuity) would imply that evolution is occurring by drift or selection, because being non-trivial implies that some members of the evolving population will fail to reproduce. However, evolution also occurs by mutation (and migration). 

For example, we can have a population at generation $1$, and each individual within that population produces one offspring, present in the next generation. This means no variation in reproduction exists. If generation $2$, the offspring of generation $1$, carry new mutations then the characteristics of generation $1$ and $2$ can differ, and the descendant generation has evolved from the ancestral state. This can be seen in mutation accumulation lines as an example:


  "In a typical mutation accumulation experiment a single inbred and
  highly homozygous line is replicated.  Each of the replicated lines is
  maintained at a very small population size (usually brother sister
  mating, or in plants, selfing).  These lines are maintained for many
  generations.  During that time mutations accumulate, and the lines
  generally decline in fitness, and the variance among lines increases." - UVM Blog


So the answer to your question, these conditions are not necessarily met in nature. However, that doesn't mean evolution can't be open ended - the conditions outlined in the paper are flawed when trying to compare to nature. Evolution can occur when the "minimal criterion" is trivial (when all individuals are capable of meeting the criteria). The existence of a non-trivial MC only implies drift (e.g. some don't reach survival to sexual maturity by bad luck) or selection (e.g. some don't reach sexual maturity because they carry a genetic disease which kills them first). A trivial MC says that there is no drift or selection, but says nothing of mutation. I have since spoken with one of the authors who describes a non-trivial MC as the same thing:


  "Regarding nontriviality, it should at least be possible that some
  individuals do not meet the MC"


Note: I have only focussed on condition 1, because this condition is not necessarily met in nature, thus your question is answered (are all conditions satisfied in nature)