How does HomeKit Remote Access work? From Apple's 2014 WWDC Conference Sessions Introducing HomeKit (Slide 11) and Designing Accessories for iOS and OS X (Slide 88), it's my understanding that a User can control HomeKit-enabled/compatible accessories even if the User isn't in the same location. I presume this means that the instructions can be transmitted over the internet and I would also assume that this doesn't require a static IP at the end location (i.e. the Home with the accessories).

If these presumptions are accurate, how does HomeKit Remote Access work? What happens when the Home's dynamic IP changes?

The only information in the presentations is that this is achieved through "iOS Device Connectivity" and this is seamless to the app developers and accessory manufacturers.
I haven't reviewed the presentation that you linked to, but there's no need whatsoever for static IP or even IPv4 connectivity for Home Kit to work.

Apple has been using IPv6 addresses and doing reverse DNS routing from the days of MobileMe and Back-to-My-Mac introduction in 2009 along with Snow Leopard. I would expect that Home Kit leverages IPv6 and mDNS (a.k.a. Bonjour) heavily to avoid the need for millions of households to establish fixed IP addresses or even set anything up other than log into iCloud on the appropriate devices.

I would also expect tight integration with Apple's Airport line of routers, but also good instructions on what settings are needed on generic or third party routers.

See Can I use Back To My Mac&#39;s mDNS address and for ssh and other routing of traffic? for more details on the existing OS X usage of mDNS.

In short, no part of the communications will depend on IPv4 as long as there is a viable network connection from the equipment running in the home to Apple's Push Notification servers so that control signals can be delivered properly.