Does this mean that when we paint 2D terrain tiles they will automatically update based upon the tiles around them?
Does this apply at runtime too when tiles are added and removed?
No it means you can make rectangular areas like buttons or UI elements that can stretch without distortion.
UI has had 9-slice rendering for a while now. Is this new update adding this functionality to ingame sprites such as terrain, or is this the same UI 9-slice that already existed in prior versions?
Try looking at the SpriteRenderer docs here.
Thanks. It seems like it is actually a new feature and not just for UI components as per the prior implementation.
Will we also be able to use this to draw with tilesets in the editor as shown here?
The purple tiles in the gif seem to be 9-slice from the Palette preview though they also seem to be able to draw additional information for internal corners which is not shown in the Palette preview image.
In this case it seems we would be limited to drawing overlapping terrain such as pictured below:
While this is nice for a start (and could be superior in the Mario example), is there any update on being able to use more than 9 slices to account for internal corners when required?
SpriteRenderer will support classic 9-slicing that lets you take single sprite, define top-right-bottom-left borders and then stretch it. Exactly like the UI counterpart.
Tilemap has more possibilities of how different sprites can tile together and has totally different approach of how to define those rules. What you are seeing in gif just happens to look like classic 9-slice.
At the end of the day, you will be able to do 9-slicing-like thing on tilemap too, it is just set up differently and is never based on just single Sprite asset (it is based on single Tile asset with multiple Sprite assets).
Yeah, commonly known as auto tile or similar 
wow ,what’s name about the tile editor?amazing~