The hadith is about the event when the Prophet ﷺ recited the Quran to the Jinn. Nearly all of the content of the hadith is present in Jami' at-Tirmidhi 2861 which is translated so you can refer to that.
As for the part about "riding" it is the statement:
فأتوا فجعلوا يركبون رسول الله
This is an idiom to express that the Jinn were crowded around the prophet, eager to listen to the Quran.
— Lane's Lexicon
The same is conveyed by the verse of the Quran:
وأنه لما قام عبد الله يدعوه كادوا يكونون عليه لبدا
And that when the Servant of Allah stood up supplicating Him, they almost became about him a compacted mass.
— Quran 72:19
And without using an idiom in the hadith of al-Bayhaqi through a different chain:
فازدحموا عليه
— Dalail al-Nubuwwah
As for the authenticity of the particular chain in the question, it has been classed as Sahih by some such as Shakir and Da'eef by others such as al-Arnaa’oot , because there are varying reports on whether Amr al-Bakali (عمرو البكالي) was a Sahabi or a Tabi and whether he learnt hadith from Abdullah Ibn Masud.