Yes, horses will need to arrive at least 1 day before the race.
The factors that AREN'T shown on that page are how much energy & fitness your horse will lose by shipping. ('Cause, you know, that'd be a bit
too easy.

)
Air travel generally takes less time, but also takes more energy/fitness out of your horse. Road travel, by contrast, is a bit easier physically/mentally on your horse, so they lose less energy/fitness.
You'll need to plan for the horse to have time to regain energy as well as train to regain fitness after arriving at a track.
Oh, and the justification for energy/fitness loss is:
Energy - the horse spends a lot of energy due to stress, fretting, disrupted diet, etc. from travel
Fitness - the horse spends a lot of time sitting around not moving
