A supra-national entity

The Holy Roman Empire, c.1600
superimposed over modern national borders.

These claims of the Empire to a unique status within Christendom were also grounded in the huge geographical extent and supra-national character of the HRE. 

Size. While the HRE is sometimes loosely regarded as analogous to Germany, in 1495 it spread over twice the area as Germany today: some 800,000 square kilometers versus 360,000 for the current Federal Republic.

Supra-national character. That vast area included substantial portions of what are now ten different European countries, including the whole of four modern states (the Netherlands, Belgium, Luxembourg, and Switzerland), all but tiny fragments of three more (Austria, Slovenia, and the Czech Republic), long slices of eastern France and western Poland (almost two-hundred kilometers wide in places), most of Italy north of the Papal States except the Republic of Venice, and also (for what it’s worth) a tiny corner of Croatia.
 
Population. The HRE was also the most populous political entity in central or western Europe.  Jan de Vries, European Urbanisation (1984, table 3.6) gives French population in 1600 as 19 million; German as 16, Austrian and Bohemian as 3.6, Netherlandish (north and south) as 1.9 million, for a total of 24.6 million, without even mentioning Switzerland or northern Italy.
 
Ethnicity and language. Given this vast extent, the empire naturally included multiple ethnic groups. German was of course the dominant language: Upper German in the higher regions to the south, Lower German in the low-lying regions to the north, the latter shading off to the northwest into Frisian, Dutch, and Walloon.  French and related Gallic dialects were spoken in western regions (notably in the southern Low Countries), Italian in numerous regional variations south of the Alps, Czech in Bohemia and Moravia, and a variety of other Slavic dialects on the eastern frontier (including Sorbian, Wendish or Lusatian in Saxony as well as Polish).  In short, the Empire was the place where the three great language families of Europe – the Germanic, the Romance, and the Slavic – came together.  It was not without good reason that the Golden Bull of 1356 (a kind of imperial Magna Carta) advised that the sons of the chief princes of the empire should learn ‘the German, Italian and Slavic tongues’.

Image: Wikimedia (CC BY-SA 3.0). 
Commentary: Howard Hotson (May 2018)