I noticed that in Galveston, TX that there is a short state highway that links SH 87 with the Coast Guard Station in Galveston. It is numbered TX SH 168.
How many other short highways that do not have LOOP or SPUR in the title does Texas have less than 2 miles in length?
TX 165 the "Graveyard Highway" is probably my favorite:
https://en.m.wikipedia.org/wiki/Texas_State_Highway_165
There are five primary highways in Texas shorter than 2 miles:
SH 165
SH 168
SH 308
SH 57
SH 223
Technically the way this thread is worded, then the Texas Park Road system qualifies here. There are many (https://en.wikipedia.org/wiki/List_of_Park_Roads_in_Texas) less than 2 miles.