How inspectlet and other services store user video sessions?
Looking at the event listeners on the page, it looks like there are a lot of bindings. For example, the <body> has scroll, keyup, and change events bound to a function. I'm sure it also has mousemove, mouseclick, etc. All of this is likely stored in a Javascript variable (object, probably) and then AJAXed every so often to http://hn.inspectlet.com/adddata with the data parameters. Here is a sample of what is being sent:
http://hn.inspectlet.com/adddata?d=mr,212941,46,337,46,1277)mr,213248,163,498,163,1438)mr,213560,144,567,144,1507)mr,213873,138,240,138,1180)mr,214188,169,184,169,1124)mr,214504,158,520,158,1460)mr,214816,231,487,231,1427)mr,215130,329,197,329,1137)mr,215444,894,289,894,1229)mr,215755,903,295,903,735)s,215755,440,0)&w=259769975&r=494850609&sd=1707&sid=1660474937&pad=3&dn=dn&fadd=false&oid=99731212&lpt=212629
As suggested in Adam's answer, they track many events in the page and send them either via a websocket or post/get request (XHR) to their servers.
I am not sure what inspectlet does specifically, but in general, such a solution will need to follow the below general steps:
When the page is fully loaded (hook on DOMContentLoaded probably) they will send the page data to the server. Then they also hook on MutationObserver in order to track all changes to the DOM in the page, so when something changes dynamically, the tracking script can 'record' it and send it to the server.
The SaaS application in turn, will have a player that will parse all this raw data and then play it back, this will usually require using some virtual file system for assests (images, css, scripts) and handling js scripts to not post back again (replay xhr will have bad results for tracked websites) but play back the mutations as they were captured (recorded)
In regards of data HTML pages compress really well, especially when you can make assumptions about the data (since you know its html) - so yes, they actually cache a lot (similar to what google does in that regards, but google does it for the entire web, not just 'customers')
The DOM Mutations will need to be stored as well. This is up to the algorithm, it can either be stored as plain text or using a smarter data model, storing them in plain text is obviously not the cost effective solution.
The above is an abstraction, there are many edge cases to handle in order to implement such a solution as well as a lot of mathematical and algorithmic thinking in regards of heatmaps to make them accurate.