What mainly keeps a partially melted scoop of ice cream from collapsing right away?

Answer: A partially fused network of fat globules around air bubbles

A viscous syrup of concentrated sugar and stabilizers — The unfrozen syrup is real and does contribute a little body, so it is a tempting explanation. But the syrup is a liquid, not a solid network, and melted ice adds water, which thins it further. It can slow flow, but it cannot hold the entire scoop upright.

A partially fused network of fat globules around air bubbles ✓ — This is the fat-stabilized foam network. Air bubbles in ice cream are surrounded by partly joined fat globules, forming a continuous scaffold that can survive some melting. As long as this scaffold holds, the scoop keeps its shape; once it collapses, the scoop slumps.

A connected matrix of ice crystals that have not melted — Ice crystals are solid and plentiful in firm ice cream, so they seem like a natural skeleton. However, when melting begins, the crystals lose contact with each other and shrink into liquid. The scoop remains standing because of the fat network, not because of any remaining crystal structure.