Unfortunately, unless evidence is found, such as proof that many other nations allow their athletes to dope or that several Western nation collaborated to humiliate Russia, this claim likely does not have a 100% provable answer. This is because it is much more difficult to prove a negative claim, such as "Other nations don't dope their athletes", than it is to prove a positive claim, such as "Russia does dope their athletes".
However, the lack of evidence that other nations dope their athletes, at least to the scale of this Russia scandal, is the best proof against the claim that this is just an effort to humiliate Russia.
The information of a single employee, Vitaly Stepanov, at Russia's anti-doping agency is what led to the investigation and evidence against Russia. So, one person in one country was all that was needed for the world to know. If Western nations did the same things that were happening in Russia, then at least one of the thousands of employees in dozens of countries' anti-doping agencies would have also come forth with evidence at some point. This evidence would be incredibly valuable to Russia and completely vindicate their actions, so the fact that they don't have such evidence means that other nations aren't doping their athletes. Therefore, it is not that the West is conspiring to humiliate Russia, rather there was evidence that Russia was cheating, so Russia was punished for cheating.
So, if someone is claiming, without evidence, that the rest of the world dopes and only Russia is punished, then the person making the claim is probably just trying to take attention away from Russia's actions through lying/propaganda, and you can ignore that person. In other words, a claim without evidence can be dismissed without evidence.