The shotgun is actually an FN Tactical Police Shotgun (TPS). It's basically a Winchester 1300 with some upgrades (AR-type sights, AR stock adapter, pistol grip). I added an Ace SOCOM adjustable stock and a Surefire lighted fore-end. The sight is an OKO red dot with the optional SC3 steel cage for Pic rails.
If you wanted a similar setup for your Mossy 590, you'd need a stock adapter from either
Cav Arms or
Mesa Tactical, the Ace SOCOM stock from
Del-Ton, and this
Surefire fore-end from Calvin at Brightflashlights (he's an Industry Partner on this site). A lot of guys with the 500/590 and the stock adapter/rails are running Eotechs, Aimpoints, and OKO dot sights. Pretty much anything you can mount up on an AR upper rail you can mount on a shotgun with the setup listed here. I'm not sure how you'd get a front sight and BUIS on the Mossy, though.
Have fun!