1.948 GL_VENDOR: Microsoft Corporation <--- this should say 'Intel'
1.948 GL_VERSION: 1.1.0
It is still saying that you're running the default Windows driver for OpenGL, which is just a placeholder/last-resort/fallback when either there's no graphics hardware present, or no proper driver for graphics hardware that's present. I suggest trying to install the 'Intel GMA' driver that I mentioned previously instead. It might just do the trick.
Also, I did find a forum post where a guy explained a solution for people with Dell Latitude laptops that couldn't get their Intel HD drivers to install properly to play Minecraft because of OpenGL problems just like you are having. His solution was to manually install the drivers instead of letting the downloaded EXE file install them automatically.
So there's two things I suggest you try. First see if the Intel HD 'GMA' driver solves the OpenGL problem: (https://downloads.dell.com/FOLDER01284336M/1/Video_Driver_W33X5_WN_8.15.10.2993_...)
If that still does not work then I believe that this guy's forum thread he started about fixing OpenGL support on Intel HD for Dell laptops might be the key. He said that instead of installing it using the driver download EXE's built-in driver installer, he said to go for the 'extract only' option beneath that - where it simply writes the files out to a user-specified destination (i.e. a folder on your desktop). From there you can go into device-manager and into the Intel HD display adapter properties, and click the 'Update Driver' button (which is visible on the last screenshot you posted). From there you can direct Windows where it should seek for the drivers you want it to install, pointing it to the files extracted from the downloaded driver EXE package. He says that after hours of trying to install drivers to play Minecraft it was the only thing that worked, and several other people replied saying that it worked for them too. I believe this sounds promising.
Similar to PixelCNC, Minecraft also has a minimum OpenGL version that it requires (and so do a lot of other OpenGL programs) so it stands to reason that perhaps the Dell driver installer for your laptop (or the specific Intel HD hardware it includes drivers for) does not work properly when it comes to making sure it sets up an installed OpenGL portion of the driver.
I believe that it's worth trying both installing the GMA driver, to see if that works, and also trying the manual installation of the driver via the 'Driver' tab's "Update Driver" button that I explained above ...and I just remembered, I read that there's also (potentially) an Nvidia GPU in your laptop - which makes Intel HD look amateur by comparison, performance-wise and in its functionality. I assumed that what I read about your laptop meant that there are certain versions of it which either include the Nvidia GPU or the Intel HD, but not both, but maybe your laptop actually has an Nvidia GPU in combination with Intel HD (Intel for 2D, Nvidia for OpenGL/DirectX graphics) and it could be the "Unknown Device" listed in your Device Manager? You could try downloading the Nvidia driver on the Dell drivers page for your laptop. There seems to be two of them, one just named 'Nvidia Graphics Driver' and then another called 'Nvidia Quadro FX .... NVS 3100 ...' Perhaps they might be worth a shot too. You're definitely going to want to figure out how to get legitimate 3D software running on your machine one way or another, otherwise the laptop as a whole will not be able to run anything but 90's 3D software :(
"Nvidia Graphics Driver" https://downloads.dell.com/FOLDER02343131M/2/E6410_Video_Driver_RHRXX_WN_9.18.13...
"Nvidia Quadro FX... NVS 3100M" https://downloads.dell.com/video/nVidia_multi-device_A08_R285549.exe
The big clue is that it still says 'Microsoft Corporation' as the driver provider, which means that there has yet to be an actual legitimate Intel OpenGL driver installed for the graphics hardware, so to my mind it's a matter of figuring out how to wrestle the proper driver in there. I think that the guy who claimed that manually installing the drivers from the Device Manager might be on to something, because I know for a fact that even the version driver you were running in Windows 10 supports GL 2.1, but it still said you were running a Microsoft OpenGL driver, so perhaps his 'trick' is the only way to get the OpenGL component of the driver to properly install for your system. (Here's the Minecraft forum thread: https://www.minecraftforum.net/forums/archive/legacy-support/1735258-dell-interg...)
Between the GMA driver, the manual driver-update, and the possibility of an Nvidia GPU hiding under your keyboard, I believe that there's a high probability that all of your efforts will pay off and you'll finally be able to use PixelCNC (among other 3D software). After you try these last ideas I can think of, and it proves unsuccessful, we can discuss what options there are for your compensation or reimbursement - for your purchase that you're unable to use. You could always hold on to your copy until you find a way to get it running, whether on a new machine, or by managing to find a way to get the driver situation figured out. But, I cannot in good conscience keep your money if you're unable to use PixelCNC, not unless you were to otherwise agree to some kind of new terms or conditions, or we come up with another specially-tailored peripheral deal first. I think that one of these ideas has to work, and that you'll be generating toolpaths like it's going out of style soon. My fingers are crossed! :D
Good luck, and godspeed!