In the reference you are quoting there is also a refutation of the existence of gravitational waves, in page 161 and 162. The reference list does not go to the LIGO experimental observation of gravitational waves, it ends in publications up to 2012. So it seems the article is pursuing an off the beaten track study of General Relativity, since even Einstein had predicted gravitational waves.
In my opinion a confusion/contradiction arises whenever one mixes frameworks of physics. What are called forces in Newtonian mechanics are connected with what are called forces in quantum mechanics only by the definition of a force as dp/dt. The three known forces of the standard model are not the only forces in quantum mechanics, every Feynman diagram with an exchange particle has a dp/dt. It is only the couplings at the vertices that can be uniquely identified as strong , weak , electromagnetic.
Physicists expect that once a definitive model of the quantization of gravity is settled ( because there exist effective models of quantization of gravity which work), the gravitational force of Newtonian mechanics will be connected with graviton exchanges.
In physics, frameworks emerge from each other smoothly in the overlap regions of the variables' phase space.
Newtonian mechanics is not thrown out because General Relativity gives more accurate results.
Classical mechanics is not thrown out because quantum mechanics explains the nucleus.
The terminology has to be careful in order not to create confusions as in the list above. The concept of force is not a necessary one for generating quantum phenomena. The concept of interactions is. When space itself is involved one cannot expect a similar path in quantization, that is why there is vigorous research on the subject.
Already there exist string theories which can embed the graviton together with the standard model of particle physics, except there are thousand of possibilities and no definite model yet proposed.