So, I'm trying to parse the grammar behind this sentence, and the lack of the article before "Éireann" is throwing me off.

Is it to be interpreted as "fir Éireann" (give on Teanglann) as "the men of Ireland/Irish men", with "Éireann" working as an adjective, attached to "Chomhthiondól", which would make "fir" shift to "fear" and add lenition because it's a definite phrase, thus giving "Comhthiondól fhear Éireann" (a meeting of the men of Ireland).

But, how does the "fir Éireann" get it's definitive reading, as issued in Teanglann, without being "fir na hÉireann"? I originally thought it was from "Éire" being definite, which "Éireann" being definite when used and thus making "fir Éireann" a definite phrase, but another post here turned me off that idea by having "banc Éireann" be "An Irish bank", which left me confused. So was my first guess correct, and it's just something that can be left out with the whole noun phrase still implied to be definite, or is there something else behind the phrase?

Interesting question.
First: ... fear Éireann instead of fir Éireann is genitive plural.
But the lenition ... comhthionól fhear ... is curious.
There are at least two reasons for non-lenition: tionól is masculine and genitive plurals tend to be unlenited.

FGB translates comhthionól fhear Éireann, as "a gathering of the men of Ireland"
and dúshlán fhear Éireann as "a challenge to the men of Ireland" (= dúshlán ar fhearaibh Éireann)
Fir Éireann is translated as "the men of Ireland".
Everything joined with Éireann is definite (with or without the article).
But comhtionól and dúshlán remains indefinite ... I'd expect the whole phrase to be definite.

GGBC refers to fir Éireann as "seanleagan"


Mar sin, is seanriail í "c. fhear Éireann"?

My own understanding is that "Fear Éireann" is a definite phrase, I've seen similar phrases referring to geographical features, e.g. Sluagh Bóinne, Iarthar Éireann. However I'm not sure how far its usage extended in Classical Irish, i.e. if any definite thing was used as an adjective did it make the noun definite.

"Fear Éireann" would then function like a definite phrase and hence receive lenition:

Chomhthiondól fhear Éireann

So basically what you two have already said. I'll try to check Classical Irish texts to see what the usage here was.

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The dialect I use is Cork Irish.
Ar sgáth a chéile a mhairid na daoine, lag agus láidir, uasal is íseal

, ar ndóigh.