At the risk of starting to sound like you-know-who ... (-;
Basically, the higher the level, the more likely it is that American law enforcement agencies will have other names than 'police,' according to their specific area of responsibility. (E.g., on the federal level: FBI, DEA, ATF, Customs, Border Patrol, US Marshals, etc.)
So 'federal police' nearly always refers to another country, and 'state police' often does.
That is, in English, the word 'police' alone normally implies the local administrative level by default: the city police. It's mainly those police officers who are called 'cops' colloquially in AE. At lower levels, other kinds of police officers in a city would include the campus police at a university, or the police force of a public school district or a public transportation agency.
At higher levels, however, there are often other words. The county police are more often called the sheriff's department, with individual officers called deputies. The state police are more often called the highway patrol or state patrol; their individual officers are (state) troopers.
*** So, if any of those terms are not in LEO, or missing the appropriate translation, they should also be added. ***
Just out of curiosity, I did a quick web search, limiting it to (site:.us OR site:.gov):
"(state OR highway) patrol" 958,000
"state police" 859,000
"sheriff's department" 626,000
"county police" 361,000
Even there, 'state police' and 'county police' may often be descriptions rather than official titles.
So, just for the record, Texas seems to be well within the mainstream, even the majority. (The only unusual group in Texas I'm aware of is the Rangers, historically the first state law-enforcement agency, now a subset of the DPS.) Different states just have different names for various agencies and divide responsibilities slightly differently. It doesn't make any more sense to assume that other states are all like New York than to assume they're all like Texas. It just varies.
To get back to the original question: I support the correction. I'm not sure a parenthetical explanation is necessary, though, since there will already be the marking [Amer.].
As for Nationalgardist, I would recommend an inclusive term, as the National Guard now obviously includes women.
If you used 'National Guardsman,' you would probably need to add 'National Guardswoman' as well, but I'm not sure either of those is all that common.