It is very fast, but how much of that is due to it being written in assembly? Isn't the real bottleneck for an application like this going to be network speed?

Hard to say, but some details about the hosting may help to estimate. The site is hosted on the cheapest possible shared hosting for 2.5€ per month: 15GB space, 150GB monthly transfer, CPU usage 30 minutes per 24 hours, 1GB RAM, max 60 processes.

I don't find it fast: page loads in 4 requests, it downloads only 16 KB and still takes several hundred milliseconds to load.

Edit: it also does not use https.