I think you are confused about the difference between the Holy Roman Empire and the Roman Empire. The map you have linked is of the Holy Roman Empire, a majority german-speaking polity; although the Holy Roman Emperor (who was always a German) nominally governed all of Central Europe and Italy, the reality was much more nuanced.

The Roman Empire, on the other hand, was a much larger Mediterranean-based empire. Its origins are in the late iron age in Central Italy, and it would come to govern the whole of the Mediterranean basin (and more!) for hundreds of years until it evaporated over the course of the fifth century. You can read our FAQs on the Roman Empire here. I wrote a few thoughts on the end of the Roman Empire, which occurred over five centuries before the map you linked, in this recent answer which might interest you.

The Holy Roman Empire, on the other hand, has its origins in the Germano-Frankish Kingdom of the late eighth century, and can be said to have definitively emerged in the late tenth century. You might have heard of Charlemagne, the ruler who built a large Empire in Western Europe in the eighth century and was crowned by the Pope; I wrote about the impact of his policies in Italy in this answer and in this more detailed follow-up. I also examined the consolidation of the German and Italian parts of that empire in the tenth century here, which is when the appellative "Holy Roman" was first used; and examined that Empire's early relationship with Venice in this follow-up. Over the course of its long history, some Holy Roman Emperors were very interested in Italian affairs, but the appellatives "Holy Roman" were largely symbolic and legal constructs; the empire was fundamentally a German one. You can read our FAQs on the Holy Roman Empire here. I also wrote this long answer examining Italy's early, and already contentious, relationship with the Holy Roman Empire that it was nominally a part of.

Would you link the map directly? It seems that you are talking about medieval Holy Roman Empire which we usually distinguish from ancient Roman Empire.