It could be small square boxes, or styrofoam blocks, or oasis (floral foam) completely covered with food-safe paper (butcher paper, cellophane, several layers of plastic wrap, etc.).
I have used the 7 inch push in pillars with a plate by Wilton for this style of cake.
It was called a "tower of roses" cake. My cake is 4 inches tall, so you have a 3 inch gap to fill with flowers. This style used to be really popular. It is a good design, so it comes back as a real classic look.
As Shanter said you can also use Styrofoam spacers. I just found the pillars to be easier.
You could send a private message to the person who made the cake (and ask.
you can also use the Bakery Crafts SPS. There are adjustable pillars that would be just fine for a small gap. I did one recently with a 4" space between tiers. the cake was very secure using the SPS. The roses were inserted on site.