Am I using the wrong driver or openGL renderer for Xeon E3-1200 v3 in Ubuntu 21.10? If so, where can I get the correct one?

I am encountering crashes in a computer game that may be due to my graphics card driver not being up-to-date. I notice, moreover, that the driver might not even be for the correct hardware, which may be due to the fact that I cloned my hard drive from another computer recently.

sudo lshw gives:

        *-display
             description: VGA compatible controller
             product: Xeon E3-1200 v2/3rd Gen Core processor Graphics Controller
             vendor: Intel Corporation
             physical id: 2
             bus info: pci@0000:00:02.0
             version: 09
             width: 64 bits
             clock: 33MHz
             capabilities: msi pm vga_controller bus_master cap_list
             configuration: driver=i915 latency=0
[...]

glxinfo -B gives:

name of display: :0
display: :0  screen: 0
direct rendering: Yes
Extended renderer info (GLX_MESA_query_renderer):
    Vendor: Intel Open Source Technology Center (0x8086)
    Device: Mesa DRI Intel(R) HD Graphics 4000 (IVB GT2) (0x162)
    Version: 21.2.2
    Accelerated: yes
    Video memory: 1536MB
    Unified memory: yes
    Preferred profile: core (0x1)
    Max core profile version: 4.2
    Max compat profile version: 3.0
    Max GLES1 profile version: 1.1
    Max GLES[23] profile version: 3.0
OpenGL vendor string: Intel Open Source Technology Center
OpenGL renderer string: Mesa DRI Intel(R) HD Graphics 4000 (IVB GT2)
OpenGL core profile version string: 4.2 (Core Profile) Mesa 21.2.2
OpenGL core profile shading language version string: 4.20
OpenGL core profile context flags: (none)
OpenGL core profile profile mask: core profile

OpenGL version string: 3.0 Mesa 21.2.2
OpenGL shading language version string: 1.30
OpenGL context flags: (none)

OpenGL ES profile version string: OpenGL ES 3.0 Mesa 21.2.2
OpenGL ES profile shading language version string: OpenGL ES GLSL ES 3.00

Curiously, while lshw says:

             product: Xeon E3-1200 v2/3rd Gen Core processor Graphics Controller

glxinfo -B says:

    Device: Mesa DRI Intel(R) HD Graphics 4000 (IVB GT2) (0x162)

These point to two different devices, so I assume I am not using the correct driver. Is that true? If so, where can I get the appropriate driver? Is one even available for Ubuntu 21.10?

EDIT: It may be that I simply need to reconfigure OpenGL to use the renderer for the Xeon processor instead of the HD Graphics 4000 processor. How could I do that?

Run sudo ubuntu-drivers devices to see which binary driver is recommended for your specific card. Try using that one:

sudo apt-get install <your_recommended_driver> # this will install the driver if no installed

software-properties-gtk # this will open Software & Updates app

There, you select the driver you have just installed.