It's trying to make the claim that these are etymological connections, which is a bit sketchy, but the phonological similarities it has meticulously catalogued are surprisingly convincing!
There are a lot of obvious cognates between Japanese and Latin through recently borrowed English or Romance words, so I was wondering what was surprising about it.
But it seems the author is talking about traditional Japanese words, and looking for ties in words and idioms like ("kokoro" & "corculum"), ("koi" & "cupio"), ("ganbare" & "quam vale"), ("omedetō" & "omen datum").
It's trying to make the claim that these are etymological connections, which is a bit sketchy, but the phonological similarities it has meticulously catalogued are surprisingly convincing!