Yes. Both creatures deal their damage simultaneously [CR 510.2].
Even if the damage wasn't dealt simultaneously, they would still both deal damage to each other because nothing dies when having damage dealt to it!! The damage is simply marked on the creature [CR 119.3e]. Shortly after, state-based actions are checked and performed. That's when the creatures are killed or regeneration occurs [CR 704.5g and 704.5h]. (All those occur simultaneously too [CR 704.3].)
(Infect and Wither cause -1/-1 counters to be given instead having damage marked. But similarly, it's an SBA that later kills the creature for having non-positive toughness [CR 704.5f].)
510.2. Second, all combat damage that’s been assigned is dealt simultaneously. This turn-based action doesn’t use the stack. No player has the chance to cast spells or activate abilities between the time combat damage is assigned and the time it’s dealt. This is a change from previous rules.
119.3e Damage dealt to a creature by a source with neither wither nor infect causes that much damage to be marked on that creature.
704.5f If a creature has toughness 0 or less, it’s put into its owner’s graveyard. Regeneration can’t replace this event.
704.5g If a creature has toughness greater than 0, and the total damage marked on it is greater than or equal to its toughness, that creature has been dealt lethal damage and is destroyed. Regeneration can replace this event.
704.5h If a creature has toughness greater than 0, and it’s been dealt damage by a source with deathtouch since the last time state-based actions were checked, that creature is destroyed. Regeneration can replace this event.