The classification came first. As Killing says in his introduction (translated by Coleman (1989)):
For each $l$ there are four structures supplemented for $l \in \{2, 4, 6, 7, 8\}$ by exceptional simple groups. For these exceptional groups I have various results that are not in fully developed form; I hope later to be able to exhibit these groups in simple form and therefore am not communicating the representations for them that have been found so far.