Ok, here goes.

Firstly, using your FTP navigate to images/arcade and create a folder called 'category'

Next in your AdminCP > Styles & Templates > Style Manager > v3Arcade Templates

Replace your v3arcade_category_bit with this:

Code:
<dd class=""><a href="arcade.php?{vb:raw session.sessionurl}categoryid={vb:raw id}"><img src="{vb:raw vboptions.arcadeimages}/category/{vb:raw id}.png">&nbsp;{vb:raw category}</a></dd>
And replace your v3arcade_category_bit_active with this:

Code:
<dd class="selected"><a href="arcade.php?{vb:raw session.sessionurl}categoryid={vb:raw id}"><img src="{vb:raw vboptions.arcadeimages}/category/{vb:raw id}.png">&nbsp;{vb:raw category}</a></dd>
You can replace the {vb:raw id}.png with another file extension if you want to use different types of image (ie {vb:raw id}.gif or {vb:raw id}.jpg)

Next you want to create the category images. The category image will correspond with the category id number; for example if you have an Action category which has the ID 8 you would name the image 8.png (or gif or jpg). Create images for all the categories and upload them to your newly created images/arcade/category folder.

I tested this using images 16x16 in dimension and 18x18 in dimension - I wouldn't recommend exceeding those dimensions but that is entirely up to you.