I would say "internationalness" is not a word.
However, I would say that in U.S. English it is considered acceptable to build new words on the spot, out of recognized prefixes, roots, and suffixes, particularly if there is no existing word that will do the job. I can't think of a good word or a shorter way to say it than "internationalness."
Checking your source, I see, too, that it is not only spoken English, but it reads as a verbatim transcript from someone who is speaking casual, colloquial English. It contains many small departures from perfect written English: "they’re speaking like another language.... I mean, when do you do that in one day, in four hours? – ‘cause that’s my goal is four hours, I always run around a four-hour marathon – so in four hours, how many different languages and nationalities and people are you able to run and come into contact with? It’s really, really amazing. It’s so international."
If I were writing or speaking carefully, with time to think, I might say "One of the other really great things about New York City is how international the race is."