No. In layman's terms it's basically this (according to my interpretation):
You're moving to a new house, packing up everything you own and making a few trips to the new place to get it all moved.
With the PS4's solution, DDR5, you basically have a box truck that drives 70 mph everywhere all the time and can hold 4,000 pounds of your shit in a trip. When you get to your destination you need to unpack all of this shit too, at 1.8 tons an hour.
With the Xbox 360 you have a big box truck that can carry 8,000 pounds of your shit but it only drives at 28 mph. You also have a car that can carry 320 pounds of your shit and can drive at 41 mph. Once you get to your destination you have to unpack all your shit at only 1.2 tons an hour, but thankfully when you go to unpack your shit is already being sorted for you by a friend outside, helping to organize how you're receiving the stuff you unpack inside.
The Move Engines are that friend. They aren't going to do any of the unpacking (read: processing). They aren't going to carry any of your shit to the new place (read: memory). They just make everything run more smoothly, helping to reduce snags and bottlenecks.
If you were very diligent in how you packed either box truck you reduce the need for such a friend, but it's sure nice to have them no matter what. Chances are the PS4 will have some level of this same concept as well, though likely not to the same extent that MS is incorporating, since MS needs some way to get over the DDR3 bottleneck.
I'd say it's a further complication resulting from MS wanting 8 GB of memory and therefore going with clearly too slow DDR3. Move Engines, ESRam, etc. are all attempts to patch over that deficiency. This is also likely why MS is running them pre-programmed, because making developers have to manage this to avoid a bottleneck the PS4 doesn't have would be a pain in the ass.
This is an excellent post. It takes real skill and knowledge to be able to come up with this clear of a metaphor for complicated tech stuff.