Yeah, it's a great thought in terms of time dilation at higher densities of mass (and thus information) as being like frame rate drops when there's a lot of objects loaded in.
The speed of light as the maximum speed of local information (gravitational waves travel at the same speed) is also similar to how games have maximum travel speeds because of memory throughput constraints (one of the big game design changes going from HDD to SSD for current gen consoles was potentially increased movement speeds).
Time dilation as you move more quickly goes hand in hand with this model too. As you move through the environment closer and closer to the speed limit for local information, your "frame rate" drops.
So moving too quickly or going near too dense of an area leads to managed frame rate drops - the rate remains steady (no spikes or abrupt drops) but decreases according to fixed rules.
It would be fun to see something like a Digital Foundry look at relativity partnering with a cosmological physicist, trying to estimate the maximum memory throughput and/or processing power of the universe based on how frame rate reduces as movement or density increases.