I've found the claim that Native Americans are predisposed to alcoholism because of their genes is false. The website cited in the claim is credible because it is a peer-reviewed journal article from the National Library of Medicine. Evidence for a Genetic Component for Substance Dependence in Native Americans - PMC
However, the article does not support the claim that genetics make Native Americans more likely to develop addictions to alcohol for several reasons. One, in the second paragraph of "Discussions and Conclusions," the study did identify that some Native American tribes lack protective variants in genes related to alcohol metabolizing, but only in comparison to gene sequences in certain East Asian and some African populations; additionally, this article then reads, "but [these missing variants] provide little overall support for the theory that Native American groups have an "unusual" metabolism of alcohol." In the third paragraph under the "Discussions and Conclusions" heading, the article says that findings in a previous study (which regards genetics as a factor of Native American alcoholism) are impossible to evaluate because it is unclear if the supposed correlation between Native Americans and substance abuse phenotypes is a cause or a result of alcoholism--the alcoholism may have developed due to environmental factors.
This journal article, another peer-reviewed and published one from the trusted National Library of Medicine, claims that findings of correlation between Native American genes and substance abuse phenotypes are questionable due to underfunded research and sample sizes too small to be generalizable for larger populations. After all, the claim that all Native Americans are predisposed to alcoholism due to genetic factors is a lofty one that forces many ethnicities into one blanket group. Genetic and Environmental Risk Factors for Alcohol Use Disorders in American Indians and Alaskan Natives - PMC
Finally, this article from The Verge, a media source ranked by Media Bias/Fact Check.com as "high" with regards to factual reporting, essentially breaks down the original claim as a myth. While many Native American communities do suffer from addiction to substances besides alcohol because of the many stressors with which they unfortunately live, such as low average income, low education levels and high unemployment, these are all external factors that do not relate to genetics. No, Native Americans aren’t genetically more susceptible to alcoholism | The Verge
Ultimately, some Native American populations may be at a heightened risk for alcoholism, but because of external factors. If a correlation between their genetics and predisposition for alcoholism does exist, it has not been found with conclusive evidence yet, and therefore this claim is false. I must reiterate, finally, that the article upon which the original claim is based (a peer-reviewed, published journal article in the National Library of Medicine) is true, trusted and factual, but the claim itself garners the wrong conclusion from the content.