Are you supposed to bring gifts for the engaged on an Engagement Dinner invite?

I would say not. The engagement present would be appropriate at an engagement party thrown by the couple but if it is to meet and greet the prospective in-laws then I don't see the necessity. The couple's engagement present can be given to them at any time and probably while out for a meal is not so convenient as giving them their gift at home. I don't see that you would be expected to bring anything for the other set of parents as you don't know them and so have no idea of their tastes. Perhaps an idea would be to contact your sister and get a feeling for how she sees the evening panning out and her expectations. Also perhaps ask your parents what their plans are. If you live away from your sister and don't see them often then maybe you would take flowers or their gift but otherwise, no. The purpose of the party is not so much to celebrate the engagement at this point as to introduce the two families.

Gifts are not required at an engagement party, though unfortunately many people think they are. But, it is perfectly acceptable to not give a gift. You don't need to bring a present to the couple or the man's parents. A card is not needed either. Why would you hand someone a card wishing them well when you are speaking to them face to face?

When you see the couple at the dinner you can wish them well. You tell the man "congratulations" but you never say that to the bride, though, again, this is something that people don't seem to know. It's considered bad form to congratulate the bride; you give her your best wishes. The reason the future groom is congratulated is that he is seen to have "caught" or "captured" the bride. Congratulating the future bride makes it seem as if she, too, had been hunting for a man and that's considered a faux pas.

EDIT: There is no such thing as an "engagement present"! Honestly, will weddings have gotten way out of hand in recent years! People have gotten so greedy. The happy couple can expect to receive wedding gifts.

That is a lovely gesture on their part. Gifts are not required for an engagement celebration. Do what you would usually do for a hosted dinner. In other words,if you usually bring a gift to a person who hosts you either at a home or a restaurant then do so. In any event, write a thank-you following the dinner.

Nope - You only need to bring a gift to a bridal shower or the wedding. No need to bring a gift to an engagement party, although it might be a nice touch.