While I cannot vouch for all of those features originating in pre-Islamic Iran (but some certainly seem to, the pointed hat is typically associated with scythians), what the author of that probably has in mind is Vis and Ramin, a Persian epic dating to around the 1st century CE (a minority opinion maintains closer to the 5th century), written down in the 11th century CE by the poet Gorgani, who notoriously went at great lengths to demonstrate his proficency in the then waning Middle Persian language. He was a major influence on Nizami, whose famous works include Khosrow and Shirin and Layla and Majnun. All of these works have been compared to Western knightly romances, above all else Tristan and Iseult, one of the quintessential knightly romances. I would also be amiss not to mention the national epic of Iran, the Shahnameh, from the same era; though it is less frequently brought up in relation to influence on European culture, it belongs to the same genre and style.

In general, heavily armored, mounted nobility who (for religious reasons) were expected exemplify virtue, were a major feature of Sasanian society and their military. I would hesitate to say that this is the definite origin of the stereotypical "knight", though, I am simply nowhere near well versed enough in medieval literature to say.

I think you can get all of these works in translation as Penguin Classics tomes; I own Vis and Ramin myself.