Nothing you posted is accurate.
"thug" is not a word of any color. I have seen it used plenty referring to white people. The primary place it is used as you claim is by leftists creating a caricature to argue against.
I haven't seen "no quarter" used, but no, no one is advocating anyone get the death penalty for "smashing windows", although that's probably the tamest thing rioters have been doing. If someone did use that particular statement, they probably are not familiar with its actual meaning in a similar way as nearly no one is familiar with the meaning of decimate or other historic terms that have no real use in modern times.
As far as arguing the President's social media messages are the official communications of the office of the President (that's a capitalized proper noun btw, I'm sure you're virtue signaling by not capitalizing it), that argument has been made by multiple leftists who were upset that he blocked them from his twitter feed.
All of that twitter bullshit is ridiculous on both sides of the argument, but it is what it is.