Good question and I agree it's confusing but no, I believe he's reffering to both adult and senior level i.e. a nationwide team.
From my view, and I'm happy to defer to Burnsie's more extensive knowledge on this, what is stopping them is the underage structure. Klub Kildare are one of the "created county" clubs that gave a pathway to the national level for underage players.
If their senior men's team was to play anywhere other than the LOI, I'm sure they'd be a lot of junior and intermediate clubs questioning why their underage age teams can't play at a national level too.
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