First of all, all methods based on "molecular clocks" have an extreme uncertainty, usually much greater than claimed in the research papers that are based on "molecular clocks".

The systematic errors that affect the published results based on "molecular clocks", always lead to extrapolated time values that appear to be much older than in reality.

The reason is that the so-called "molecular clocks", i.e. the rate in time of inherited mutations that we can see in the DNA of currently living organisms is not a constant, neither in time nor between different living beings.

This variability of the inherited mutation rate is handled by calibrations based on known fossils, but this helps only for interpolation between known calibration points, not for extrapolation in the past beyond the oldest calibration point.

The rate of DNA mutations varies only slowly in time, mostly because the ambient radioactivity has decreased continuously from the formation of the Earth. I do not have access to the research paper linked here, so I do not know if they have attempted to compensate for this factor. Most likely they have not, so this already provides an overestimation of how old are the genes for oxygen consumption.

However the rate of inherited DNA mutations is only a small part of the original rate of DNA mutations, because most mutated organisms are non-viable or non-competitive. How many mutations are inherited can vary greatly between species. Some organisms have better DNA repair mechanisms than others, but usually the greatest factor affecting the variability of the inherited mutation rate is how great is the competition for the mutated organism, wherever it lives.

When competition is intense, few mutants survive. Otherwise, e.g. after a catastrophe that has wiped out the competition, or after invading a new environment, the competition is reduced and many mutants survive, having the chance to accumulate additional mutations that remove their handicaps. This leads to systematic overestimation of the times in the past of the genetic changes that have happened around mass extinctions or around the invasions of new environments.

In conclusion, without being able to read the research paper, there is a great probability that they have overestimated the time in the past when the genes for oxygen utilization have appeared.

That said, a small amount of free oxygen has already existed in the environment forever, before the apparition of the oxygenic phototrophs. That free oxygen is produced mainly by the ultraviolet light of the Sun, which can decompose the oxygen containing molecules, e.g. water and carbon dioxide.

So it is plausible that bacteria living in places exposed to air have evolved means to dispose of the toxic substance that was free oxygen, i.e. enzymes that catalyzed some harmless oxidation reactions.

However it is unlikely that bacteria have become able to use free oxygen as a source of energy before it became really abundant, as a result of the activity of cyanobacteria (blue-green algae). One reason is that the primary enzyme used for binding free oxygen uses copper. Copper was much less abundant in the environment before free oxygen became abundant, because it was bound in sulfide minerals.

However, it is also possible that the copper enzyme has been a later addition to the respiration chain, providing an extra oxidation stage that has increased the energy efficiency, i.e. the amount of useful energy that is generated per each consumed molecule of oxygen.

In this case, there has been an older less efficient version of the respiration chain, using only iron enzymes, which could have appeared before free oxygen was abundant.

Nevertheless, as long as free oxygen was only a small fraction of one percent of the air, as it was before the appearance of the oxygenic phototrophic bacteria, free oxygen could have been only an extremely minor source of energy for the biosphere.