Do I miss some story points if I don't watch Kingsglaive and Brotherhood before starting the game?

You can play Final Fantasy 15 without watching Kingsglaive and Brotherhood, however this Reddit post does recommend that you watch Kingsglaive and Brotherhood to gather back story and context

I strongly recommend watching Kingsglaive and Brotherhood before starting the game.

Call it a failing on the part of the opening but I felt the game doesn't do a very good job of easing you into the story and who is who. It kinda just feels like your thrown headfirst into Noctis's journey without any kind of context or backstory save a scene or two in the opening scenes.

Don't get me wrong, I am loving the game but I couldn't believe how much backstory I would have missed if I had not watched Kingsglaive and Brotherhood. They really should have included them along with the standard edition of the game as they are kinda crucial for getting up to speed on what's gone down and who the main characters in the game are in terms of their personalities and their relationships to Noctis.

The wikis Kingsglaive and Brotherhood also contain developer comments towards the movie and anime and state you can watch them independently without playing the game.

Kingsglaive: Final Fantasy XV is a feature-length CGI film set during the events of Final Fantasy XV. It was officially revealed during the Uncovered: Final Fantasy XV event, and is 110 minutes long. According to developers, one can enjoy Kingsglaive: Final Fantasy XV without playing Final Fantasy XV, and vice versa. Experiencing both tales, however, ensures a deeper level of appreciation for them, as they are intended to complement one another.

Brotherhood Final Fantasy XV was conceived by marketing producer Akio Ofuji and the director of Final Fantasy XV Hajime Tabata, as a method to introduce the game's main characters and to help people better understand the game's character dynamic. Prompto in particular was subject to scrutiny, as he had ranked low in fan polls. Tabata has stated that while a typical role-playing game gradually assembles its cast, the heroes of Final Fantasy XV are together from the start. Brotherhood Final Fantasy XV shows how Noctis and his friends came together; developers hope the series would allow fans to familiarize themselves with the characters before playing Final Fantasy XV.

Absolutely not. The game stands on its own.

However, if you don't watch Kingsglaive, make sure you read the Lore Tour in the tutorial. It covers some important things that otherwise don't come up until the very last few chapters.

I went in blind and got all the way to the end of the game without ever feeling like I was getting an incomplete experience. Absent Kingsglaive, the motivations of some characters may feel underdeveloped, but any game events that don't make sense will be explained by the end of the game.

Kingsglaive does touch the plot. In particular (early-game spoilers and possible Kingsglaive spoilers)

It explains how Lunafreya gets the Ring of the Lucii.

But that explanation isn't important to Noctus' story.

That doesn't mean the movie and anime aren't worth watching in their own right, in the same way that Rogue One is worth watching even though it's not necessary to understand A New Hope.