That area has been a predominantly low income, minority community for many years, but since it is close to downtown, it has been "gentrified" in the most recent years. Most of the old low income houses have been replaced by 3-4 story town homes.
Turkey Leg Hut has been open for 3 years, but it is possible those houses have been there for less than that. A majority of the houses down there are new construction these days. I wouldn't assume that the houses were there before TLH showed up and started puffing smoke. It is more likely the other way around.
Houston is a no zoning city as well. You can buy a house that for some reason has an auto repair shop right next to it or something similar. Really random at times. We are kind of funny like that and it drives out of towners and new residents nuts.
Also, a lot of these people that are buying these new homes seem to have a strong sense of instant entitlement that their perfect environment should not be infringed upon in any way. I live in a different inner city area of Houston. There is a new development a couple miles from me with a bunch of 3 story town homes (really nice too) right next to a train track. Well these home owners are blowing up the local Nextdoor board complaining about the train horn. Hello, you bought a house next to a train track!!
All that said, if you are running a fire that is billowing out that much smoke, maybe you can learn better how to run a clean burning fire? Maybe a brethren could drop by and preach the gospel of thin blue smoke. But maybe any smoke smell at all is too much in the eyes and noses of the residents. Some people just like to complain. But that is a huge amount of smoke coming out of those pits so something should be done to run cleaner by the pitmaster. At least it should be possible.
The thing that surprises me is that this guy is allowed to operate at all. The city of Houston is notoriously strict on restaurants. It is extremely difficult to open a restaurant in Houston without a ton of headaches and red tape. Houston is very left leaning and has tons of government types ready to dip in your pockets.
If I am rambling here, apologies. just trying to lend some insight into my home town.