There is a long laundry list of specific requirements in order to be considered an eligible library, archive or museum that qualifies for the DMCA exemption, which you also have to apply for and continually renew: https://www.federalregister.gov/d/2021-23311/p-191

Here are just some of them:

(ii) For purposes of paragraph (b)(3)(i) of this section, a library, archives, or museum is considered “eligible” if—

(A) The collections of the library, archives, or museum are open to the public and/or are routinely made available to researchers who are not affiliated with the library, archives, or museum;

(B) The library, archives, or museum has a public service mission;

(C) The library, archives, or museum's trained staff or volunteers provide professional services normally associated with libraries, archives, or museums;

(D) The collections of the library, archives, or museum are composed of lawfully acquired and/or licensed materials; and

(E) The library, archives, or museum implements reasonable digital security measures as appropriate for the activities permitted by paragraph (b)(3)(i) of this section.

I would also argue that it doesn't matter whether itch.io itself is one. An archive hosted on that platform isn't any less of an archive.

According to the DMCA, legally, it does matter, because there is a very clear definition of an "eligible archive" that itch.io does not meet for the exemption to be valid. You also have to apply for the exemption explicitly, and renew it regularly.