The headword appears to be nominative or accusative plural of an unattested noun θαλαμακεύς , unless this form (also unattested elsewhere) is simply a mistake for θαλάμακες , nominative plural of θάλαμαξ (see n. 1); cf. theta 8, theta 454, theta 455, and generally Morrison and Coates (1986): 132-151; Casson (1995): 82-4.
[1] Dative singular of θάλαμαξ (Web address 1); the form, a variant on the more common θαλαμιός or θαλαμίτης (Web address 2), appears at Aristophanes, Frogs 1074 (Web address 3), and much of this entry comes from the scholia on that line. Cf. Hesychius theta19, Etymologicum Magnum 441.24.
[2] It does say the other three ranks, even though there are only three ranks in total (as described below).
[3] If this is not a misunderstanding, or a description of the manning of some ship other than a trireme, then it perhaps refers to the fact that of any vertical rank of three rowers on a trireme, the uppermost man will be situated astern of the middle man, and the middleman astern of the bottom man.