The "rules" apply to dinner in the dining room. If you are skipping that, dress neatly, but any way you want. IMHO, jeans & a cruise don't really go together, however. Opt for anything else & be comfortable.
My defensiveness only jumps in when people wrongly assert that because they plopped down $x thousand, the suggested dress code shouldn't have to apply to them. You are coming from a completely different place. There are plenty of alternative dining venues.
BTW, "formal" on a cruise ship is not necesarily equal to "Formal" in NYC. This isn't opening night or a $500 pp charity ball that's being photographed for the Times or Town & Country. You will see people dressed to the nines, but you'll see other perfectly acceptable clothes. If you can manage a sexy sundress, strappy sandals & great jewelry or a blue blazer over good slacks , if you are a man (I don't want to make assumptions based on your screen name), you should be deemed to have achived the bare minimum.
If this is your 1st cruise, my suggestion is that you pack the dressiest thing you could stomach putting on while vacationing. It might just be acceptable for formal night . That last statement is admittedly an East Coast prejudice.