I asked that same question years ago, and IIRC I was told to ship it upright....
I forget the exact reasons given, but IIRC it's the monitor that is the issue.
And I can say I've never seen an arcade cab shipped laying down.
That said, if you can't secure it upright, it's better to ship it laying down that to let it puzzle bobble off your trailer and get destroyed.
Oh, and one last piece of advice... don't transport it with a giant steel safe sitting next to it...