Board game art is beautiful (well most of it). I know a lot of people who would love to hang board game art on their wall or wear the design on a shirt. Merchandising seems out of reach for a small business but there is a way. An easy way.
Redbubble is a print on demand website. It’s similar to Etsy but way better. On Etsy, you have to create your own inventory and ship to your customer. Not on Redbubble.
Redbubble basically has a warehouse full of blank shirts, blank mugs, blank posters, blank notebooks, blank stickers, etc. You simply upload your artwork onto their website and choose which products you’d like the artwork to be available for. That combo of art and product is now listed on the website. A customer scrolls through all the listings, sees your design, buys it. Redbubble then prints your artwork on to the desired product and ships it to the customer. You didn’t have to do anything except simply make your artwork available. It cannot be easier.
Making an account is free. There is no reason not to upload your art. You already have the art, might as well upload it. If the shirt sells for $20, you’ll probably make $2. Easy money. Plus, now someone is walking around as a billboard for your game. Just being listed on Redbubble itself is free advertising for your game. That site gets a lot of traffic.
There are many print on demand websites. While I encourage you to use all of them, some may be a better fit for you art. Look into TeePublic and Merch By Amazon.