I agree it's a crappy intersection, but I'm pretty sure this person just has an old utility right-of-way on their 'property' and they are trying to get the city to abandon it. There is no way they would just close off the street here.
Compare the outline of the house on the south side of the intersection with the outline from the HCAD map and that person has fenced in that entire triangle that belongs to the city. Old satellite photos from google maps show it used to be a driveway/road of some sort.
Key learning here, if you want the city to give up its land, just build a fence around it and call it yours for long enough.