I don't speak Polish, so I can't speak to specific claims made in the video, but nonetheless, claims of 'empire' are certainly nonsense. We know some things about the early Slavs--not a lot, but some. What we know is not consistent with an 'empire' of Slavs covering the territory in that map (which is, when you actually take a closer look at it, only superficially similar to the other map you link).

The problem with supposing a Slavic presence in the area marked in that map in this time period is that it is only in the sixth century that the Slavs start to unambiguously show up in Classical documents. Before then, there are mentions of various tribes of uncertain origin who can only be very tenuously established as Slavs. Why should that be, if there was this enormous empire of Slavs right there? Well, as Schenker (1995) says, "The lack of contacts between the Romans and the Slavs could not have been accidental. It can be explained simply by the fact that the Slavs, unlike the Celts and the Germans, had not arrived on the frontiers of the classical world until after the Great Migrations."

So, what do we know about the early Slavs? Schenker (1995) has a quite exhaustive list of classical accounts mentioning the Slavs, and the quotes below are taken from him.

Well, the Slavs start showing up in the historical record in the sixth century. Jordane mentions them in his history of the Goths (ca. 550):

Near the left ridge [of the Carpathian Mountains], which inclines toward the north, and beginning at the source of the Vistula, the populous race of the Venethi dwell, occupying a great expanse of land. Though their names are now dispersed amid various clans and places, yet they are chiefly called Sclaveni and Antes. The abode of the Sclaveni extends from the city of [Noviodunum](https://en.wikipedia.org/wiki/Noviodunum_(castra)) and the lake called Mursianus [Schenker suggests Mursianus refers to the delta of the Danube - rusoved] to the Danaster [Dnestr], and northward as far as the Vistula. The Antes, who are the bravest of these peoples dwelling in the curve of the Back Sea, spread from the Danaster to the Danaper [Dnieper] rivers that are many days' journey apart.

So, here we have the term Sclaveni, which is a Hellenized version of the Slavic endonym *slavěni--Greek didn't like sl clusters, so they put in a /k/. The other two names are of less certain origin. Veneti belonged to a different tribe living around the Vistula in previous times. Antes was possibly the name of an Iranian tribe which either became Slavicized or otherwise associated with the Slavs by their neighbors. Schenker suggests that the geographic distribution of these tribes "may prefigure the dialectal division of Slavic", and while this is tempting, it is perhaps too good to be true.

Schenker gives several other 6th and early 7th century accounts of the Slavs, and the picture they paint is of a loosely-organized society ("they have lived of old under a democracy", according to Procopius; "they are independent, absolutely refusing to be enslaved or governed", according to the Strategikon); they are a "sturdy people"; they are skilled at navigating rivers; and they have effective military tactics, favoring javelins, small shields, and ambushes.

A final note: The two maps you give are both problematic; the first map has the Slavs expanding into France and the Low Countries, which is pretty fanciful--the western extent of the Slavs in the second map is more in line with what I understand to be the case. On the flip side, the second map obscures the fact that the Avars were a sort of multilinguistic federation of tribes with a strong Slavic component. It also presents the Danube as a sort of firm boundary, but the Slavs had started raiding across it by the middle of the 6th century, and by the middle of the 7th century, had established settlements in the Balkans down to the Peloponnesus, from the Black Sea and Aegean to the Adriatic, even besieging Constantinople with the Avars and Persians in 626.