No, this piece does not purport to be about the first time ever a troll was mentioned, but rather the first time we have a record of somebody writing about a troll.
The term troll is distinctly elusive of definition, because it has been applied to all manner of creatures in Scandinavian lore - giants, bigfoot-type creatures, diminutive beings, helpful beings,witches, harmful beings, even beings deemed to look pretty much human. They are generally said to be ugly. As for the Bigfoot-like kinds, one 19th Century commentator suggested there were wild folk still living in the woods of Sweden who were behind alleged sightings. Sometimes it was said trolls could not stand daylight and, if exposed to it, would turn into stones or trees or even burst asunder.
The first troll we have mentioned is in a poem by Bragi (9th Century). He engages in a verbal exchange with this creature, who is female. Unfortunately, he provides no description. Bragi himself was regarded as the first poet among the Norse. Later, we find a poetry god named Bragi, whose name probably came from that of the poet. This god, however, may be a literary invention, not worshiped in heathen times.