In standard usage, sentence-final "though" (optionally preceded by a comma) is used where the current sentence or phrase qualifies or limits what was said earlier. E.g., it might point out a flaw or drawback, or conversely a silver lining or mitigating circumstance.
- He's handsome. Kinda dumb though.
- It's beautiful. Real expensive though.
- Forrest Gump wasn't very smart, but he was honest though.
This is slightly informal, more common in speech than in writing. Note that it cannot be substituted with "although" in this context.
The usage you noted, which does not involve any prior sentence and is often written with "dat" and "tho" or even "doe", seems to be a modern Internet meme usage.
The website Know Your Meme discusses the "dat X tho" meme and credits one particular viral Vine from 2013 for popularizing it. See the link, the dialog is:
- [Purse snatcher grabs a girl's purse and runs off with it]
- "Help, my purse!"
- "I'll save you!"
- [Would-be savior performs a useless stunt instead of helping to catch the thief] "Woo hoo!"
- "He's already gone."
- "Yeah but that backflip tho."
The fact that he skillfully executed a backflip is humorously presented as a mitigating circumstance for criticism that he failed to act to stop the crime.
Urban Dictionary has an entry for "dat ass doe" (i.e., "that ass though"), expressing the thought that if a girl has a pleasing posterior it mitigates the fact that her face may not be so pretty or her intellect substandard. In other words, there is an implied and unspoken earlier phrase.
However in practice, I think "tho" is sometimes simply added gratuitously to the end of a "dat" phrase and then its usage morphs to be just an emphatic particle. Perhaps like sentence-final Canadian "eh?", except without the rising tone.
Sorry for the above example, but Urban Dictionary didn't have another less sexist "dat" phrase to cite. Know Your Meme mentions that "dat ass" itself probably originated on the 4chan website circa 2009.