The National Guard is only part of the state militia. Most states have one or two other components. One is an organized group usually called the State Guard, the other is the called variously the "Reserve Militia" or "Unorganized Militia". Texas has both. I don't know if Arkansas has a State Guard, but I'd guess they probably do.
In the years I've been in Texas the State Guard has gone from barely organized and rarely used to a well organized part of the State Defense forces, including both an Army and Air component. They help run the armories of the National Guard, especially when the Guard called into federal service. They provide disaster relief and serve other functions as well.
The Reserve Militia portion is males 18-45 in Arkansas, it's all legal residents 18-60, male and female, except a few defined public officials.
And then only when the feds let the state borrow it. Various court cases have determined that a governor has no power over his state's National Guard, if the feds want to use it for something. All guardsmen, and I was one long ago and in far away land (called Oklahoma), are also dual hatted as members of the federal military reserve. Those officers that are to be appointed by the governor according to the Constitution are mostly, but not entirely, people commissioned into the federal military, or in most cases into the federal reserves (ie. ROTC grads, OTC/OCS graduates, or even Academy grads). Those few actually appointed by the states still have to be "federally recognized", which means that the feds could not recognize them, and thus have a veto over what is a power of the states as defined by the US Constitution.
So it's something of a legal fiction that the National Guard is even a part of the State Militia.
That's not true of the State Guard, which is a true militia (although most of the officers are still former federal military officers (but then again George Washington was once an officer in the British Royal Militia). But even the State Guard is not "The" State militia or "the Militia" it's only part of it.
Ohio is another example...they obviously have their National Guard, but also have an Ohio Organized Militia (state-sanctioned) and UOMA (Unorganized Militia of Ohio.)
Fincher apparently was claiming to be part of the general, unorganized militia; however the state made their case on the fact that he wasn't part of the State Militia.
He may be 60, and officially too old to be part of the "militia" but a true patriot is militia until he dies of old age.
If I remember correctly Texas has some trump cards. Texas is the ONLY State that was a sovereign nation prior to joining the Union. There is even a school of thought that Texas could succeed anytime they wanted by election.
Here in Nevada the Militia has to be defined and authorized by the Governor. That goes back to the days when some silver barons had basically their own armies and argued that they were "Militia".