TL;DR: Everything should give everything. There should be no "Fleet Gameplay", or "Romulan Gameplay", or "Borg Gameplay". There should be only Gameplay.
I'm not sure what their goals are for "fleet gameplay" but so far every activity that awards fleet marks is way too easily farmed solo. If fleets are supposed to be social, my doing it in a pug with no one else from my fleet, or just doing it alone (duty officer mission, pvp, daily fleet mark mission, or the nowdefunct investigate officer report) seems to me like it would completely defeat the purpose.
In my mind "fleet gameplay" is anything I do teamed with a fleetmate. Be cool if we got fleet marks attached as a reward for any mission completion we do teamed with a fleetmate.
All teh rest though, I agree, should just be gameplay.