Understanding USBHID_DESC report
It's pretty easy to follow if you indent and break it up right.  Let me add some annotation too:

Usage Page Gen Desktop Ctrls(01)  // Usages describe what the
Usage Game Pad                    // following data is used for.
Collection Application
    Usage Pointer        // Use the settings for a physical
    Collection Physical  // pointing device
        Usage X       // It has four axes - 
        Usage Y       // X, Y, Z and some other undefined axis.
        Usage Z
        Usage Undef
        Logical Min(80) // Output the values 0x80 to 0x7F, which when
        Logical Max(7F) // interpeted as signed bytes is -128 to 127.
        Physical Max(FF00) // The input has a range 0 to 255
        Unit(0000)
        Unit(0000)
        Report Size(08)  // The report value is 8 bits long, 
        Report Count(04) // and there are 4 of them (one per axis)
        Input(00000010)  // This ends this "input" section. 
    End Collection

    Usage Hat Switch // Describing a HAT Switch now.
    Logical Min(01)  // Interpret it as a value between 1 and 8
    Logical Max(08)
    Physical Min(00) // The input to it is between 0 and 0x3B01.
    Physical Max(3B01) // Not sure that value is interpreted properly.
    Unit(14)
    Report Size(04)  // The report has 4 bits in it, 
    Report Count(01) // and there is just one of them.
    Input(00000010)  // And end the input section.

    Usage Page Button(09)  // Next come the buttons.
    Usage Min(01)      // These are basically button numbers
    Usage Max(04)      // - there's 4 buttons, 1 through 4.
    Logical Min(00)    // A button is either off (0) 
    Logical Max(01)    // or on (1).
    Report Size(01)    // And can only have one state, so size 1.
    Report Count(04)   // There's 4 buttons, so 4 reports.
    Input(00000010)    // And end the input.

    Report Count(08)   // This is a special one. It keeps the settings
    Input(00000001)    // from before (the haven't been changed), but
                       // is just a dummy one to pad out the data to
                       // the right size. Alignment is key.

    Usage Page LEDs(08)    // Now we have 4 LEDs with an 
    Usage Slow Blk On Time // 8-bit PWM value. 0-FF which doesn't
    Logical Min(00)        // need interpreting, so 0=0 and FF=FF.
    Logical Max(FF00)
    Physical Min(00)
    Physical Max(FF00)
    Report Size(08)    // As I said, 8 bit,
    Report Count(04)   // and there's 4 of them.
    Output(10000010)   // And it's output.

    Unit Exp(00)   // Now there seems to be a bit of junk.
    Unit(00)
    Unit Exp(00)
    Unit(00)
    Unit Exp(00)
End Collection Game Pad // And the end.


So interpreting that, you get a report sent to you that has:

Byte     Function
0        X Axis 0-255 which you map to -128 to 127
1        Y Axis 0-255 which you map to -128 to 127
2        Z Axis 0-255 which you map to -128 to 127
3        Another Axis 0-255 which you map to -128 to 127
4        Upper 4 bits buttons, lower 4 bits HAT direction
5        Padding byte to make ita multiple of 16 bits long


And you can send a 4 byte report where:

Byte     Function
0        LED 1 PWM
1        LED 2 PWM
2        LED 3 PWM
4        LED 4 PWM


Those "LEDs" could be force feedback motors or vibrators.

Also I suspect there is maybe a small amount of corruption or mis-interpretation of multi-byte values in the output.