Proof of concept blender addon for controlling the viewport with a gamepad (evdev python module needed, only tested under linux)

gamepad-control.py

bl_info = {
    "name" : "Gamepad Control",
    "author" : "István Donkó",
    "description" : "Control the blender viewport using a gamepad",
    "blender" : (2, 80, 1),
    # "location" : "View3D",
    "category" : "Generic"
}

import bpy
from mathutils import *

# Getting evdev

import subprocess
import ensurepip

ensurepip.bootstrap()
pybin = bpy.app.binary_path_python
subprocess.check_call([pybin, '-m', 'pip', 'install', 'evdev'])

#

import evdev

def get_device():
    device_list = evdev.list_devices()
    if (len(device_list) > 0):
        return evdev.InputDevice(device_list[0])
    else:
        return None

# device = evdev.InputDevice('/dev/input/event26')

# rv3d = bpy.context.screen.areas[5].spaces[0].region_3d
# rv3d = bpy.data.screens[2].areas[3].spaces[0].region_3d

# for area in bpy.context.screen.areas:
#     if area.type == 'VIEW_3D':
#         if context.active_object.mode == 'EDIT':
#             area.spaces[0].use_occlude_geometry = True

# device.absinfo(0).value

# mode = 'absolute'
mode = 'relative'

def view3d():
    return bpy.data.screens[2].areas[3].spaces[0].region_3d

class GamepadControl:
    # def __init__(self, device):
    def __init__(self):
        self.data = []
        # self.device = device
        # self.rv3d = bpy.data.screens[2].areas[3].spaces[0]

    def get_axis_value(self, i):
        return (self.device.absinfo(i).value - 128) / 128

    def check_gamepad(self):
        # while (event := device.read_one()):
        #     v = (event.value - 128) / 128
        #     e = rv3d.view_rotation.to_euler()
        #     if event.code == 2:
        #         # rv3d.view_rotation.y = (event.value - 128) / 128
        #         # print((event.value - 128) / 128)
        #         rv3d.view_rotation = Euler((v*5,0,0)).to_quaternion()
        #         # e[0] = v*5
        #     if event.code == 5:
        #         # rv3d.view_rotation.x = (event.value - 128) / 128
        #         rv3d.view_rotation = Euler((0,0,v*5)).to_quaternion()
        #         # e[2] = v*5
        # rv3d.view_rotation = e.to_quaternion()

        [a, b, c, d] = map(self.get_axis_value, [0, 1, 2, 5])
        # print([a,b,c,d])
        if (mode == 'absolute'):
            # rv3d.view_rotation = Euler((b*2,a*2,d*2)).to_quaternion()
            view3d().view_rotation = Euler((b*2,a*2,d*2)).to_quaternion()
        if (mode == 'relative'):
            # rv3d.view_rotation.rotate(Euler((b*0.1,a*0.1,d*0.1)))
            speed = 0.05
            view3d().view_rotation.rotate(Euler((b*speed,a*speed,d*speed)))
            # rv3d.view_distance += c
            view3d().view_distance += c
        # return (1 / 30)

gamepad_control = GamepadControl()

def main_loop():
    gamepad_control.check_gamepad()
    return (1 / 30)

def register():
    device = get_device()
    if device:
        # gamepad_control = GamepadControl(device)
        gamepad_control.device = device
        # bpy.app.timers.register(gamepad_control.check_gamepad)
        bpy.app.timers.register(main_loop)

def unregister():
    # print(gamepad_control)
    # if gamepad_control:
    #     print("asdf")
    if(bpy.app.timers.is_registered(main_loop)):
        bpy.app.timers.unregister(main_loop)
    # if(bpy.app.timers.is_registered(gamepad_control.check_gamepad)):
    #     bpy.app.timers.unregister(gamepad_control.check_gamepad)