I meant structure as in existing stuff, not 'structural' as in load-bearing. Extra wood would indeed still count as 'structure' within the context I meant.

This is, however, not just extra wood. What was cut through in the picture is floor joists, which are what holds up the flooring and supports whatever is on the floor, including people and furniture. Cutting these joists severely compromised the integrity of the floor. Now instead of a squeak from stepping in that spot, it's far more likely that a loud crack followed by a fall through the floor will be the result of a heavy step.