For ParlorGames -- that "dress for dinner" thing?! A popular misconception! And not our cup of tea either! We have done it, and some folk love it, the girls having some fancy frocks, and the gents in a tux (which I hated!). I'd guess there would be 2 or 3 'formal wear' nights on a 2-week cruise? The rest of the time, well, smart casual is OK, and some lines won't like it if you turn up in swimwear and flipflops?!
BUT -- ships have a buffet, in use for b'fast and lunch, and for evening meals too (though some folk don't realise the latter), in which they'll likely have most of the options that the Main Dining Room has, but you serve yourself, not have someone bring it to you. They may even have a few other options, so if you didn't like the look of the Main Menu that night, use that venue.
PLUS -- you don't have to 'dress up', and you CAN if you fancy have 3 starters and 4 puddings?!! (etc etc).
If you're there late enough, you'll see the dancers and maybe cabaret turn up for their supper.
Assuming you prefer 'smart casual', Fred Olsen caters for the 'more mature' British customer, on ships that are usually much smaller than many on other lines, and I've seen women in cardies having dinner, blokes in braces maybe? Azamara run small ships with wonderful service levels, 'smart casual' throughout (unless they've changed) and not quite at full '6-star' prices, though if your budget runs to those, then you can have a great experience (just 'smart casual' if you like) on the likes of Regent, Oceania, Seabourn and similar lines.