Blue coming in you can ( bounding text to rectangle for size and animating in )
Blue getting smaller while adding white not (as there is no way to resize text on the fly, resizing bounded rectangle based on text as such not)
White resizing based on text change yes (but not with the extra white space at beginning of rectangle being different than before ) , same as blue : text bounded to white rectangle)
Resizing text to fit within a textbox is possible but cannot bind the rectangles to be different colors for each row of text
The second white text animation can be simulated with a datachange ( when text changes)
btw reference to white and blue i mean the backgrounds

in short: NOT like the example

The closest to simulating this is with legacy XAML titles and some binding within the title and probably some extra coding

Be ORIGINAL ;-)