That doesn't sound like any version of GATE I'm familiar with. Just sounds like your usual public-school-run daycare. Admittedly GATE seems to have always varied a bit from state to state. There's also been some contemporary difficulties with the program in the post-Obama Common Core era where much of the former GATE curriculum now is standard. So, you may have gotten a stripped-down version because much of the logic/math bits are now the normal way those subjects are taught. If you go on the CA GATE website you can see teachers bitching about this, or not understanding what they're doing that's special anymore. So, it may just have been the timing of your program.
In contrast, in my experience during the Clinton-Bush era, GATE was a full curriculum of classes that were administered separately. When I was in it, everything revolved around groups and group work, including my grades. This used to drive my parents batshit because they couldn't understand how those grades worked. There were occasional field trips, more than the other students got, and we spent a good deal of time playing various computer games. Projects involving architecture were also something we did. I only know these bits and pieces because I have documents (and software) supporting them. In truth, I don't remember much.
When my parents were in GATE (yes, it's that old), it was a twice-weekly after-school program. They can't recall much about it either, outside of the fact that they also had frequent field trips. Both of my relatives from this version of the program work in the quasi-public sector. One works for Lockheed. The program was temporarily shut down during the fervor over school integration. Apparently, the people running it thought it would be totally destroyed for being racist. Obviously, that didn't happen.
From what I've dug up GATE is the descendant of a Cold-War era piece of legislation that was passed into law at the same time DARPA and NASA were established, during the Eisenhower administration. It's right in there with them in the legal code. The law itself is very bare-bones, but clearly paves the way for the program as it's known today. Furthermore, the characteristics of a "gifted child" as described in contemporary publicly available documents match the Cold-War era IPAR (run out of UC Berkeley) profile of a "creative individual". All of this is stuff I've posted before in /gatebreakers/.
Whatever went into that program was extensively researched and developed for decades. Be dismissive at your peril.
Outside of the initial GATE discovery threads, follow-up threads tended to be full of demographic shitposting without new research or content. And, at this point, the threads are also well-known enough that new demographic information and personal stories are unreliable. Muddying the waters or making the people reporting their experiences seem delusional. You can see this happen if you read through the archives. It starts with people listing weird coincidences and being perplexed and slowly moves into full-blown /x/ craziness after several initial threads untouched by that.
What's needed are more contributions like the OP pic, where people can find some actual documents and previously unknown connections. Unfortunately, this is probably something individual anons will have to do on their own because of the physical records involved. It's not like some leak dump where all of the relevant material is already on the internet.