The two-barrels discharging at once clearly comes from the fact that the COP .357 prop in Brion James’s hand was modified to fire two barrels at once to enhance the muzzle flash effect (which would have led me to speculate that the weapon is not intended to be interpreted as a simple Derringer, but … oh, well).
So they do not fire in a “burst”; they fire simultaneously. The stats must therefore describe the compound effect of two bullets.
The way the text is written, the weapon can fire exactly twice between reloads. Call that “four shots” if you will; for my own part, I will not.
And as for that semantic discussion … yes, there is confusion due to the fact that in one meaning, “shot” can be used synonymously to “round”. But that is not “the” definition; merely “a” definition — the word has multiple meanings. For which reason I repeat: if you mean “4-shot capacity” in the specific meaning of “4-round capacity”, then saying “4-round capacity” will cause less confusion.
“Flavour text” or no.
Before you use the word "XENOMORPH" again, you should read this article through: