The original Transport Tycoon predated DirectX and ran on DOS. Later games like RollerCoaster Tycoon had basically the same UI and were also almost entirely written in assembly (despite now running on Windows rather than DOS), so it's clear that Sawyer pretty much did write a graphics library in assembly.

If I remember right, the Windows versions of RCT, which descends from TT/TTD, use DirectX to allocate their framebuffer.

Then they just operate directly on it, because the engine literally is older than DirectX.

Transport Tycoon (Jun 1994) was published over a year before the first version of DirectX (Sep 1995).

No it has talked directly to SVGA cards with help of BIOS VESA calls.