I am sorry for such a broad question. I am wondering if there are any tools to make drawing icons / images like the image below. Ideally something quicker than drawing lines, boxes and circles in photoshop?
Illustrator is the real alternative to Photoshop for that kind of graphics and for icons.
But you'll still draw lines, squares and circles! At least it should be way easier to manipulate, move and transform these shapes with Illustrator than Photoshop, and how you fill them will colors as well. Photoshop is better for photo-montage and to deal with pictures than graphics; it's not easy to do illustrations from scratch with Photoshop since its tools are still quite basic for this purpose.
Illustrator (or any other vector software) creates vectors which offer you the possibility to resize and transform your artwork easily and without any loss of quality. It's more versatile than Photoshop for that kind of graphic.
But unfortunately, technology isn't at the level of offering any better alternative yet than using simple shapes, assemble them and create an illustration out of it! With some practice and good tutorials, you will end up appreciating the freedom of using simple shapes and lines gives you!