So i found this A while ago and it claims to be the anthem of the Roman Empire. I would myself doubt that since the empire existed before nationalism and classic music. But could there still have been some sort of Roman anthem maybe a military anthem?
The ideas of anthems, countries, nationalism, and so on as we know them are recent. National anthems became popular in the 19th century, and there are some dating from the 18th century (the Netherlands did it before it was cool, in the 16th century).
I don't know anything close to a Roman anthem. To be honest we don't know much about the actual music from back then, but something like an anthem would be pretty well known if we had evidence of it.
Vegetius tells us, in a text from the late 4th century, about musical instruments used in the military... We have depictions (in monuments) of instruments and the soldiers using them, those would be wind instruments similar to trumpets. Those are loud, the obvious choice for outdoors.
The music from the video you link ("The Final Legion") seems to be from a 2008 album by Triarii (a musical collective, of the "martial industrial" kind, from Germany). Not even remotely related to anything Roman, as far as I can hear or read.
The closest you might come to an "anthem" for the Roman Empire would be for the Byzantine period, and would be the Orthodox Troparion of the Cross, "O Lord, Save Thy People". composed and written during the Byzantine period of the Roman Empire and still used frequently in Orthodox Churches:
O Lord, Save Thy People/Σώσον Κύριε τον λαόν σου
The translation is...
O Lord, save Thy people and bless Thine inheritance, Grant victory to the Emperor over the barbarians, and by virtue of Thy cross, preserve Thy habitation.
It was an "anthem" of sorts, used both in church on feasts of the Holy Cross, days and events of national/Imperial significance and in battle.
Though the modern version is different (since neither the Roman Emperor, nor the Russian Czar exist), it remains a sort of anthem for the Orthodox Church.
The older Russian version translates roughly as:
O Lord, save Thy people and bless Thine inheritance, Grant victory to the God-fearing Czar over his adversaries, and by virtue of Thy cross, preserve Thy habitation.
Since the overthrow of the Czar, the Russian version was changed to:
O Lord, save Thy people and bless Thine inheritance, Grant victory to the Orthodox Christians over their adversaries, and by virtue of Thy cross, preserve Thy habitation.
Just for curiousity, here is a video of the Russian composition:
O Lord, Save Thy People/Spasi Gospodi, Iyudi Tvoya
Famously, the Russian version was used in the 1812 Overture in the opening and closing (along with "God Save the Czar").
The masterful composition of the 1812 Overture including the hymn in it.