Does steel have to melt for fire to weaken a building?

No. Melting and weakening are different things. Heated steel can lose strength and stiffness well below its melting point, so a fire does not need to turn beams into liquid metal to affect a structure.

That still does not explain a collapse by itself. The relevant questions include how much structural damage occurred, how heat spread over time, and how the building carried loads as parts were damaged.

A demonstration that puts steel in molten metal is a poor model for a building fire. It tests whether intense heat can melt steel, not how localized impact damage and fires might affect connected structural components.

And the fact that damage starts in a limited area does not mean any later failure must stay limited to that area. Loads can shift to other parts of a structure. The specific sequence needs evidence and structural analysis, not just a comparison to a pool of molten metal.