Some films in the cinema certainly have a recap of sorts. Consider the opening of The Lord of the Rings: The Two Towers for example, where we see a repeat of Gandalf's falling scene, which is then extended to show the new film from The Two Towers showing what happened afterwards.
However, I would suggest the reason for this not being generally done is for three primary reasons:
It's generally not needed
Films are (generally) much simpler than their TV series counterparts. This is quite logical, due to the fact they are much shorter, and often with far fewer characters. Consider your The Hunger Games example with a TV series like Game of Thrones, with all of its twists, complexities and characters. Whilst a recap sequence for The Hunger Games might be nice, all of the films are generally understandable without this.
On top of that, for films broken into two parts, most people wouldn't see the second until they had seen the first (and if they hadn't seen the first, most wouldn't be sympathetic at not understanding the second!). If they did see the first, then even if they forgot some events from it, the second film shouldn't be completely alien to them.
It shouldn't be needed
If a film series becomes so complex it is unintelligible without intimate knowledge of the previous few films, it will likely stall at the box office as new viewers will be unfamiliar with it. Remember, new TV series episodes are released weekly, compared to new films which could be yearly. Watching three seasons of a series may take you back a couple of years. Watching three films may take you back six or seven years, or more. To try to counter this, "connected" films like The Hunger Games, The Lord of the Rings etc have been released annually, with much smaller gaps between them - but it's still a year gap, as opposed to a week. Therefore, the films have to be kept largely meaningful without having recap sequences.
After all, if a new film, with a massive budget, is created targeting only people who will have that intimidate knowledge of what has happened previously, it will seriously reduce its box office potential. Even film series like Harry Potter, with eight films, were understandable without the previous films and worked as standalone films. This made them far more marketable and would have increased their revenue potential.
It breaks immersion
TV series are a very different beast to films. Most series have breaks between them for ads (with the likes of ad-free series on channels like HBO still fairly new)1. We are watching them in our own houses. They (generally) have lower budgets than films, with less well-known actors.
Compare this to a cinema trip to see a new film, in a big room, with a huge screen, with high budgets and big name stars. It's a very immersive, satisfying experience. Putting recap sequences in front of each part of the film would definitely break this immersion.
1: @Tetsujin rightly commented that the BBC has offered ad-free television for decades in the UK - however, as the majority of the mainstream TV series are produced in the US, I feel this point still holds true.
