What happens when a creature with "Whenever a creature dies" dies simultaneously with multiple other creatures?
Yes, Marchesa's ability will save herself if she dies with a +1/+1 counter, along with other creatures who died at the same time as her that had a +1/+1 counter. You are correct that rule 603.6d is the reason for this.

Basically, 603.6d says the in normal circumstances, whenever something changes, all objects that now exist are checked to see if any of them trigger. BUT, it says that leaves-the-battlefield triggers work differently. With leaves-the-battlefield triggers, the game must look at what the gamestate was like just before the event took place to see if the event caused any triggers to go off.

In this case, after all creatures die, the game checks to see what things were like just before they died. And now that the game is looking back in time, to just before the event happened, it sees Marchesa as an object that has a triggered ability that should trigger as a result of this event; in fact one that should trigger multiple times, once for each creature with a +1/+1 counter that died.

Hope this clears it up!

603.6c is how you know that "dies" triggers count as "leaves-the-battlefield" abilities:


  603.6c Leaves-the-battlefield abilities trigger when a permanent moves from the battlefield to another zone, or when a phased-in permanent leaves the game because its owner leaves the game. These are written as, but arent limited to, "When [this object] leaves the battlefield, . . ." or "Whenever [something] is put into a graveyard from the battlefield, . . . ." An ability that attempts to do something to the card that left the battlefield checks for it only in the first zone that it went to. An ability that triggers when a card is put into a certain zone "from anywhere" is never treated as a leaves-the-battlefield ability, even if an object is put into that zone from the battlefield.


(Note that "dies" means "Whenever [something] is put into a graveyard from the battlefield".)


  603.6d Normally, objects that exist immediately after an event are checked to see if the event matched any trigger conditions. Continuous effects that exist at that time are used to determine what the trigger conditions are and what the objects involved in the event look like. However, some triggered abilities must be treated specially. Leaves-the-battlefield abilities, abilities that trigger when a permanent phases out, abilities that trigger when an object that all players can see is put into a hand or library, abilities that trigger specifically when an object becomes unattached, abilities that trigger when a player loses control of an object, and abilities that trigger when a player planeswalks away from a plane will trigger based on their existence, and the appearance of objects, prior to the event rather than afterward. The game has to "look back in time" to determine if these abilities trigger.