The words are Latin, the pronunciation is (approximately) Italian.

Google's language tools are very, very bad at some languages, and for Latin they are especially bad. By bad I don't mean 'lots of mistakes', I mean 'incoherent gibberish'. I'm surprised it managed to get the names of the numbers right.

Having said that, Italian pronunciation wouldn't be the worst possible approximation, and Latin in late antiquity would be starting to make transitions to what's in the video in some respects. The word stress patterns are the same in both languages, and imitating the way Italian deals with long vowels is a decent approach.

The main differences are:

• the letter v (like in viginti): in Italian, like English /v/; in classical/aristocratic Latin, like /w/; in late Latin, both were possible.
• the letters c and g before a front vowel (decem, viginti): in Italian, like English /ch/ (tʃ) and /j/ (dʒ) before i and e; like /k/ and /g/ otherwise. In classical Latin, consistently like /k/ and /g/. In late Latin they started gaining assibilation before front vowels, that is to say something like /ks/ and /ts/, on their way to transitioning to the Italian pronunciation.
• final m (like in septem, decem) and n before a stop (like quinque): final -m isn't a thing in Italian, and you can hear the voice resorts to vocalising the end of the consonant (almost adding an extra syllable). In classical Latin, final -m and n before a stop were nasal, and final -m could even be omitted. You can hear a similar phonology in Italian in m before a stop (ampio), and in final -n (con, un poco).
• vowels: long vowels aren't used consistently in the video (e.g. trēs), though they do appear in ūnus and quīnque.

While we know a lot about letters' sound values in Italian Latin, there are plenty of aspects of phonology where we don't know a whole lot. I mean things like: how much the Romans trilled /r/, or the extent and circumstances in which /s/ got voiced, or the extent to which they used ejective consonants. (Note: this is off the top of my head, and an expert in Latin linguistics might actually have something to say about these examples!) We've got a certain amount of approximation in our knowledge of Latin pronunciation, and we know register (and class) made big differences. But we can certainly do a lot better than what this tool has produced.

The best guide to Latin phonology is still Allen's Vox latina. It's fine as far as it goes, though it isn't nearly as detailed as what linguists have to say about modern languages.

Edit: I should add that many modern people use localised pronunciation customs for pronouncing Latin, which vary from country to country: this is especially noticeable in Latin sung in classical music. Latin in Italy, Germany, France, and England are all noticeably different. German Latin, for example, treats c before a front vowel as /ts/; Italian and English Latin treat it as /tʃ/, and French Latin treats it as /s/. French Latin treats r as a French r. And so on.

Edit 2: it's always nice to have occasion to tell a story, and maybe I can share the shock that I felt when I first realised what is going on with the choral Latin in Parry's piece I was glad. This is a coronation anthem used for British monarchs since Edward VII. In the middle of the piece, the choir breaks into Latin and sings (e.g. for Elizabeth II) 'vivat regina, vivat regina Elizabetha'. But the pronunciation is that of early 1900s English Latin, which is roughly where modern lawyers' Latin comes from. In classical Latin this would be

wee-wah-t reh-gee-nah

and in modern English choral Latin it would normally be

vee-vat re-jee-na

But for this one piece, choirs customarily sing

vie-vat rih-jie-na

in imitation of the pronunciation used at the coronations in 1953 and earlier.