Okay, I don't think JRE has anything to do with this, not directly at least, because I've done the following and I still can't start 3.8.99:
1) Uninstalled all JRE versions (32 & 64) and Spine
2) Rebooted the computer
3) Installed both JRE 32 & 64 bit 1.8.366 version
4) Installed Spine Launcher
5) Asked to launch 3.8.99 and got the SAME error
Then I went to another computer in my home, and installed Spine there, asked to launch 3.8.99 and it downloaded and ran the thing just fine.
So, it's obviously a problem with this Windows installation, sure, but I don't know how to troubleshoot this, because that "Assistive Technology" that it not found in the log, seems to be something that was supposed to be integrated into Java already, according to what I've Googled.
I'd appreciate any suggestions on how to proceed to fix this. I'd very much like not needing to install another Windows, because if I do that I'd also need to do the same with Unity, and that would be... tricky, to say the least.