Does Tiny G replace Serial Ports?

I am sort of new to build-it-yourself CNC, so am not sure what you frame of reference might be.
TinyG is a Gcode to Stepper motor interface, correct.
It connects to a hose computer, via USB.
Machine and GCode parameter configuration is stored in tniyG, but Gcode must be streamed to the tinyG.
Some folks have interfaced tinyG to external drivers; search the forum and Wiki.
When I first entered this activity, the primary options seemed to be Parallel Port interfaces (e.g. LinuxCNC) and USB. I am not familiar with any serial solutions, but as said, sort of new.

Simple answer : yes

More complex answer – as I understand it, with parallel port to stepper interfaces, the parallel port lines connect to stepper drivers, essentially a hardware interface function.
tinyG interprets Gcode, does acceleration and movement planning and interfaces directly with steppers. So tinyG does some of the intelligent work done by PCs driving parallel ports.

tinyG implements third order motion planning.
A similar product, Gshield and GRBL, FW running on Arduino Uno, performs similar tasks, but using second order motion planning.

Both interface to computer via USB.

Both are probably equally challenging to interface to external drivers.

HTH

I have never looked hard myself, but have read discussions of others that leads me to believe you have to pick off the inputs to the on-board drivers and extend them / interface them to your externals.
I do not believe it is as easy as connecting the tinyG outputs (motor winding switches) to your external drivers.

This post in in the tinyG sub forum.
Back up to the “Forum” level, then enter External Stepper Drivers in the Search box. You see several posts on the topic.