it used your strength stat for the damage, as it did for all melee capable aliens. TU usage was later changed to like 15%, probably in order to give melee aliens a fighting chance, otherwise they'd rarely if ever have enough TUs left over to make said attack.
at some point it was decided that they would hard-code which aliens were melee capable and which were not, and the ability was removed from the player as well.
i'd guess that the reasoning behind this decision was that melee capability caused ranged enemies to act in silly ways, like charging the player instead of shooting from cover (this behaviour can be observed in TFTD with lobstermen, as the AI remained largely unchanged), and that the code was never really finished (melee accuracy wasn't ever factored in, for example).
TFTD actually did fix the code to use melee accuracy, and added hand drills so the player could use melee, but the enemies were similarly hard-coded to be melee or not. but in this re-incantation it was only added to special melee type weapons, most likely because all memory of this early beta feature was lost to the ages.
source: the source. and a lot of makin shit up.