Our brains bounce around in time constantly. Every time your eyes microsaccade, your brain is filling in the gaps after the fact with the best guess at what you were looking at, hence why periodic movements can be "elongated" when you first look at them (look at a clock and the second hand lingers a bit long for the first second).
Our brains absolutely do not need to process things in chronological order, but it seems we have evolved for our egos to believe we do, for evolutionary advantage (although, in the last few thousand years we've been doing everything we can to do an end run around that).
Our perceptive unconscious or pre-concious self does not need events to be in order to assemble a meaningful stream of cognition but I'd argue our conscious layer does. The part of us that has the ability to believe or not believe things is by definition a modeling appliance. It takes in information from the outside world through the various interfaces available to it and uses that information to build a causal model. It's often wrong, but it does fundamentally want to see the universe as this happens which has caused that in the past which means that this other event may have a similar outcome. I wonder if this modelling appliance is a major part of the ego and what we consider the 'self'.
At some point, the ordering of events _has_ to become 'information about the ordering of events' and once that happens, they no longer need to be in order.
Our brains absolutely do not need to process things in chronological order, but it seems we have evolved for our egos to believe we do, for evolutionary advantage (although, in the last few thousand years we've been doing everything we can to do an end run around that).