Watching this tournament has me thinking this will likely become a bigger and bigger deal in the coming years. It's too good of idea for what is otherwise a major lull in the sporting calendar (i.e. the summer) for it not to grow from here.
On the game: Diebler hasn't been much of a factor given his possible injury. I was thinking he might be necessary to beat this Marquette team.
More evidence in support of "The Dodgers probably moved this game to Friday" hypothesis: this 1957 Ohio State-Illinois program listed future schedules for 1959 in which this game was on October 3rd instead of October 2nd.
Did some more background reading into that odd-ball 1959 game at USC and why that was on a Friday. Best explanation we could conjure highlights the scheduling bottleneck at the Los Angeles Coliseum at that time. Four teams shared the venue in the late 1950s---USC, UCLA, the Los Angeles Rams, and the Los Angeles Dodgers---and USC appeared to shift some of its games to Friday early in the season as a result.
1959, in particular, was a trying year for scheduling events in the Coliseum. The Dodgers, then in their second year in LA, were in the World Series and played Game 3 at the Coliseum two days after USC hosted the Buckeyes. The Dodgers could very likely pull rank on scheduling venues at the Coliseum, forcing the college teams to Friday.
Alas, it's conjecture but it's a likely explanation. It's still a conspicuous event in Ohio State's football history all the same.