IMO, I don't think you can say that it's clear they lived happily ever after. Are we supposed to believe that the both Castle and Beckett look exactly the same "7 years later" and didn't age at all from their present day looks? To me, they sure didn't look like they aged in that montage at the end of the episode. If you are going to flash forward 7 years in the future, at least have the characters look a bit older especially since they would be in their 40's with that 7 year leap.
I also think the choice of "7 years later" from the writers is interesting. Why not choose 5 years, or 6 years or even 10 years ? But they chose 7 years instead. Since the show premiered in March of 2009, the choice of 7 years later would bring us to today in 2016. I see the ending of the episode as Castle "the writer" looking back on meeting Beckett in 2009, remembering their first exchanges and wondering what would have happened had Beckett originally excepted his invitation to diner. Had she agreed right away then things would have turned out differently, i.e. they would have fallen love and got married much quicker. Then "7 years later" in 2016 they would still be married but this time with kids living happily ever after instead of lying on the floor in the present day about to die.
