The platform / browser sniffing is done in JavaScript. You can glean the code directly by looking at a launch page's source. For Inquisit 4 Web, see e.g. view-source:https://www.millisecond.com/download/library/v4/IAT/IAT.web
The functions of interest are in the
/*****************************************************UTILILTY FUNCTIONS
******************************************************/
section towards the bottom (starting around line 950).
Hope this helps.