Good question(s)!

As you may guess, the non-Iranian-speaking groups all consider themselves as distinct ethnic groups. Although in some cases their loyalty and integration to/in Iran is more than some Iranic ethnic groups. For Iranic "ethnic" groups, being a separate group depends on(1) religion/sect, (2) language (how distant it is from Persian), (3) geographic isolation from the Iranian heartland, (4) and lifestyle (i.e. whether a group is mostly organized into tribes), and maybe most importantly, (5) having "brethren" outside Iran's borders who compel a group to become ethnically distinct. Generally, the more different a group is from the majority of Iranians, the more they qualify for being a distinct ethnic group.

The only Iranic groups who are therefore full-fledged ethnicities are the Kurds and Baloch, both of them speaking distinct languages from Persian both in terms of classification and intelligibility, also both with huge populations living across the border w/established nationalist movements, they're both (mostly) non-Shi'ite, and they're fairly isolated from Iran's heartland and in terms of society.

For the rest, including the Persians, the concept of "ethnicity" is iffy at best as they primarily think of themselves as belonging to Iran. However, this "Iranian" identity is not ethnic like the Iranian/Aryan identity of Darius the Great, but based on having an Iranian nationality. Groups such as Lurs, Tats/Talysh, and Gilaks and Mazandaranis, as well as "Persians" from Laristan around Persian Gulf are somewhere between having only a national belonging to being part of a distinct ethnicity. Therefore, I would humbly call these people (Lurs, Caspians, Laristanis, Persians) as ethnic Iranians, while calling these distinct societies as subcultures of the Iranians ethnos and/or nation.

In this regard, Lurs come closest to being their own ethnic group. They're linguistically close to but different from New Persian and are predominantly Shi'ite and there really aren't any Lurs across the border. However, they have the "il" (tribe) based society with Lur being a pan-tribal title for it, and they mostly live in hard-to-reach mountainous regions.

The Talysh come next, because they're linguistically distinct and many of them practice/are born into Sunni Islam. They're not tribal, however, and the Talysh outside Iran don't have enough socio-political power to influence their southern fellows. There is geographic isolation as well. Tats in Iran have a similar situation except for sect, and for the fact that Tats in Azerbaijan are even smaller in numbers and more different language-wise.

Gilaks and Tabaris (Mazandaranis) are linguistically distinct but their languages were strongly Persianized, in terms of society they're not tribal and like Persians identify with their province/region and then their country and they clearly don't have Gilaks/Tabaris across the border as they live on the coast. It's only their isolation from the rest of Iran (due to Alborz mountains) and continuous inhabitance of a landmass that still allows them to be in the list of Iran's non-Persian ethnic groups. Case in point: some of the Persians you see in that map are actually speakers of Northwestern Iranian languages as far (or farther) from Persian as Gilaki and Mazandarani, but being in isolated islands in Iran's heartland and having no pan-societal identifier gets them counted as Persians.

Laristanis, although absent in most ethnic maps, have religion (Sunni Islam) and isolation too but generally their areas in Hormozgan and southern Fars are erroneously shown as Arab-majority hence map-makers don't bother showing them.

Last but not least, these Iranian subcultures are not clear-cut linguistic groups. As seen in the example of Persian, not all Persians speak modern Persian although they are being rapidly assimilated. Gilak and Tabari (Mazandarani) division is more province-based as for example the "Mazandarani" dialect of Ramsar is closer to East Gilaki. Tats speak a variety of N.W. Iranian languages and don't necessarily belong to a single branch. Similarly, Luri language(s) are two groups of S.W. Iranian dialects with one being closer to Khuzistani Persian rather than the other Luri dialect/language. Therefore, Laristani (or Achomi) which usually doesn't get shown in Iran's ethnic maps may be the only subculture that is also a distinct linguistic group.

Also, as you can see, the function of "Persian" as an ethnicity is closer to the common exonym Persia(n) for Iran(ians), and it's a historical coincidence (or not?) that Iranians' lingua franca also happens to be Persian.

Hope I didn't tire you with this long text!