Title II of the Civil Rights Act of 1964 prohibits discrimination on the basis of national origin in a place of public accommodation. In Noah v. AOL Time Warner, Inc., 261 F. Supp. 2d 532, it was ruled that a website is not a place of public accommodation with respect to that law. The opinion explains why a website is not a "place", as described by the law: they "are limited to actual, physical places and structures". There are opinions regarding websites as public accommodations w.r.t. ADA, which is a different law. However, physical grocery stores are places of public accommodation, and most grocery stores have signs in one language and staff who speak one language, perhaps English, Spanish, Russian... so there is a potential analogous question about stores.
A website in English discriminates against those who do not speak English, who may have a non-US national origin (though don't necessarily). Also, a website in Norwegian will discriminate against many people who are not from Norway. Since language tends to correlate with national origin, even if a website does not deliberately set out to discriminate against people of Chinese origin, it may have that effect if the website is in English.
There is a doctrine of "disparate impact" applicable in discrimination law. This arises for Title VII (employment) for instance Griggs v. Duke Power Co., 401 U.S. 424, which held "if, as here, an employment practice that operates to exclude Negroes cannot be shown to be related to job performance, it is prohibited, notwithstanding the employer's lack of discriminatory intent". Hardie v. NCAA is an apt case directed at the Title II prohibitions, in this case involving attendance at tournaments and racial discrimination, founded on a disparate-impact theory. The NCAA prohibited convicted felons from serving as coaches, and plaintiff argued that the effect of such a policy was racially discriminatory (most felony-conviction denials were African-American). The opinion clarifies that neither SCOTUS nor the 9th Circuit have decided whether disparate-impact claims are cognizable under Title II. Some courts have found that Title II authorizes such claims. So it is presently not resolved whether a disparate impact claim could stand in for direct national-origin discrimination (or religion, or race or color).
Given current law, websites are not required to be multilingual in order to avoid having a disparate impact in terms of national origin, at least until there are definitive rulings to the contrary (expanding disparate impact doctrine and the concept of "public accomodation"). I doubt that will happen any time soon, but it's not ludicrous to think that such changes could happen eventually.
Language discrimination is a viable basis for an employment discrimination lawsuit, and EEOC regulations presume that English-only workplace rules violate title VII. So there is a recognized legal connection between language and national origin.
On the face of it, it is immaterial that speakers of English could learn Chinese so as to be serviced at a Chinese-speaking store, or that speakers of Chinese could learn English so as to be serviced at an English-speaking store (or website). Race, color and national origin are facts that you cannot change (things get murky when you consider self-identification as a basis for racial classification), whereas religion is something that you can clearly decide to change: and yet discrimination on both types of grounds is illegal. On the other hand, requiring all websites to accommodate to all languages would be a plainly unreasonable burden on commerce and expression.