As /u/y_sengaku's good answer says, that brief chapter more really refers to the Rus' and Crimean Goths in one way or another. I think there's some valuable context in Snorri Sturluson's Trojan origin myth featured in the prologue of his Edda, at the end of Gylfaginning and in Ynglinga Saga, where the Æsir were people who came from Troy to the vicinity of Crimea and Tanais in the Don delta, and from there to Scandinavia and were ultimately the progenitors of the Germanic peoples (or at least their rulers).
Although it was taken at greater value once upon a time, I don't think, and I don't think most historians today think, that Snorri's story here has much historicity to it. Rather, he was working within the long tradition of Trojan origin myths to put the Scandiavians on the same footing as the Romans and French and Normans and others who'd claimed such origins.
Now, it's very likely the Scandinavians knew about the Crimean Goths. They lived after all along the highly frequented route to Miklagarðr (Istanbul) and also routes that went from the mouth of the Dniepr up the Don to Tanais, and possibly further to the Caspian. It'd only take a modicum of interaction to realize the language where 'man' and 'hand' was 'manna' and 'handa' was much more closely related to their own than the Slavic and Turkic languages in the vicinity. Once you have the idea there are distant relatives of your people along the Austrvegr, the field is open to come up with stories about how that came about. We don't know what the Crimean Goths own story was either, but the fact that the Gutasaga and Ynglinga Saga have nothing in common - the migration going in opposite directions even - is certainly as good an indication as anything that this is not drawing on a deep tradition going back to the Goths' supposed Scandinavian origins. Rather, it appears to be separate attempts at explaining the fact of the Crimean Goths, who'd they'd become aware of during the Viking Age when Scandinavians (particularly Swedes and Gotlanders) began to travel the Eastern Route to the Greeks.
If they really understood fully who the Goths were, it'd also be a strange omission to leave out Theoderic who was already a subject of medieval legend. As opposed to later Swedish Gothicist historiography which was all about bragging about how the Goths had supposedly originated in Sweden, but only came about in earnest in the Renaissance when Swedes became aware of the Gothic history of Jordanes (who claimed an origin for the Goths in Scandza in the 7th century) etc.
Jordanes' account has always been the #1 reason for the alleged Scandinavian origin of the Goths. That, and the likely common etymology of Goths (Gothic *guta) and Gotlanders (Old Gutnish gutar) and Götar (Old Norse gautar) of southern Sweden. Of uncertain origin but often hypothesized to be a term for 'men' related to Proto-Germanic *geutaną ('to pour'.. as in men are the ones who 'pour' semen) We can't regard this as separate evidence though; Jordanes, like the later Gothicists, may have assumed a common origin on the basis of the similarity in names and perhaps only a vague knowledge of some sort of Baltic-area origins. His writing shows knowledge of peoples in southern Sweden; but it may have been information he'd gathered from contemporary sources on the basis of presuming an origin there. It's known for a fact that he conflated the Gets (or Getae) of Thrace with the Goths, so it becomes very plausible his entire Scandinavian origin was based purely on name similarity here too.
As /u/y_sengaku said, the first we know of the Goths is that they were living on the Baltic coast of present-day Poland. There's no consensus that they really originated in Scandinavia; although they did likely have close ties with Scandinavia.
To get back to the Gutasaga though; The story is linked to the Rus' and Byzantium, both of which are Viking Age concerns. It is much more likely a conflation of the contemporary Rus' origin story (which Nestor had written down a century earlier) with the contemporary Crimean Goth origin theories, than a rare record of a far more distant event that may not have happened.
I'm not sure whether the relevant passage in the chapter 1 of Gutataga describe the alleged migration hypothesis of the Goths from Gotland that has been almost completely refuted (or cannot confirmed in any way and they tend to begin the history of the Goths instead from the 3rd century Black Sea) among the specialists, or the more general expansion of the Norse people across Russia and NW Eurasia (i.e. the Eastern Road of the Vikings) since the 8th century, as cited below:
They could not support themselves there either, but travelled up by the watercourse called the Dvina, and onward through Russia. They travelled for such a distance that they came to the Byzantine empire (Grikland). There they asked permission of the Byzantine emperor (konungr, lit. trans: the king) to live ‘for the waxing and waning’. The emperor granted them that, thinking that this meant no more than a month. After a month had passed, he wanted to send them on their way. But they answered then that ‘the waxing and waning’ meant ‘forever and ever’ and said that was just what they had been promised. This dispute of theirs came at last to the notice of the empress. She then said, ‘My lord emperor, you promised them that they could settle for the waxing and the waning of the moon. Now that continues for ever and ever, so you cannot take that promise away from them.’ So there they settled and still live. And, moreover, they retain some of our language (Peel (trans.) 1999: 5).
The chapter 2 of GS deals with the relationship between the Gotlanders and the ruler of mainland Sweden up to St. Olaf expelled from Norway in the 1020s, and chapter 3 concerns with the transition from the heathen rites to Christianity, so I suppose the latter is more likely. It means that the supposed age of the this migration myth into Eastern Europe, allegedly transmitted orally, did probably not date further back to the Late Antiquity, belongs rather to more recent period like the Viking Age.
References:
(Edited:) fixes typos.