From a purely economic standpoint, it would make some sense on the distributor side. Compared to other consumer products (think cars and furniture), the depreciation on a HUO pinball machine is very low, so if you retain a security interest in the machine and get 20-30% down, the collateral protects the creditor unusually well on default. The problem is that consumer credit law is not uniform (geographically segmenting the market) and there are huge economies of scale arising from regulatory costs---a problem for pinball distributors whose clients are geographically disbursed.
Probably the only way to implement consumer credit for pinball machines would be to partner with a lending institution and arrange the transaction through a credit credit card (putting all of the regulatory costs on a bank that can handle them more efficiently).
You commonly see those arrangements from distributors of consumer products up to about $2000. Something about the $5k price point likely makes the arrangement uneconomic. If I had to guess, it would be that debtors who would qualify for and care to take advantage of this sort of thing are outside the risk sweet spot for CC co's (whose profits generally are derived from neither their riskiest nor least risky debtors).
(Obviously, as others have pointed out, financing the purchase of a pinball machine is a really terrible financial decision.)