The Imperial alphabet is just an unusual font of romaji, i.e. Latin alphabet. Most of short inscriptions are in English, e.g. "God", "Original forest", "Home town" etc. However the word "sorry" on the wall in Episode 19 is written as "gomennasai", i.e. in Japanese. The "keep out" poster in Episode 2 contains the English word "Warning" and following the Japanese text written in "romaji-style". The proper names are written like Japanese romaji, e.g. "Arunusu" for Alnus. Looks like the authors have some fun mixing English and Japanese texts.
While I believe that the Humans of the Special Region started out as mostly Romans speaking Latin, it seems little beyond names remain as recognizable Latin. Many of the 6000 prisoners taken in the Ginza Incident were questioned by language experts before the JSDF was sent thru the Gate. I have to believe that such experts would have noticed if there was much Latin in the language. Languages change over time. Thru daily usage and exposure to other languages. Old French and Old English (of about 1000 years ago) seem to have little in common with modern French or English.
The Humans who first crossed the gate have been isolated from others who spoke their language for almost 2000 years. The other people of the Special Region organially spoke languages that had no connection to the languages of Earth.
Time, usage, isolation from other speakers of the language, and exposure to other exotic languages, have left the Special Region with a pretty much unique language.
Roman Latin didn't changed much between 500 BC - 376 AD on the main Lands (Italia). This first happend when Italy was conquered by germanic Tribes like Ostrogoths, Langobards, Franks ect. The romanized Regions (Hispania, Gallia, Britannia and Dakia) developed dialects (called vulgar Latin) which lead to Spanish, French and Romanian. Italian developed from the mix of roman standard Latin with the germanic languages gothic, langobadian and frankish which influced mostly northern Italy (Cisalpina). Later the tuscan dialect from the north became standard Italian (which was based on a form of vulgar latin, heavy influced by the occupation of germanic tribes in the late antiquity and early medieval).
I guess the mainlands with the capital of the Empire is speaking late classic standard Latin while the Border Regions have their own forms of vulgar Latin, mixed with the pre Empire native languages. Now with the "occupation" by the JSDF their stanard latin will influced by japanese language.