If I simultaneously kill my opponent and deck myself at the same time, is the game drawn?
It's a draw.
While the 'lethal' effects do not occur simultaneously, the state-based actions that check whether a player loses only happen after the spell resolves, not during its resolution:

608.2. If the object that's resolving is an instant spell, a sorcery spell, or an ability, its resolution may involve several steps.
116.3b The active player receives priority after a spell or ability (other than a mana ability) resolves.
704.3. Whenever a player would get priority (see rule 116, &quot;Timing and Priority&quot;), the game checks for any of the listed conditions for state-based actions, then performs all applicable state-based actions simultaneously as a single event.

After Electrolyze resolve, state-based actions are checked:

104.3b If a player's life total is 0 or less, that player loses the game the next time a player would receive priority. (This is a state-based action. See rule 704.)
104.3c If a player is required to draw more cards than are left in their library, they draw the remaining cards and then lose the game the next time a player would receive priority. (This is a state-based action. See rule 704.)
104.4a If all the players remaining in a game lose simultaneously, the game is a draw.