It's the movie sequel to the Steins;Gate anime TV series. It's not as excellent as its progenitor, but it's nice and it manages to find an acceptable way of continuing a story that had come to a very definite end.
Do you need to watch this film? No. It doesn't really add anything. It resets a central relationship, in order to spend the rest of its running time building it up again. (I didn't mind this too much since it's logical and in-character for both of the idiots in question, but it's still a reset and I'd been assuming that they wouldn't slip back like that.) Okarin's back to being a dysfunctional whacko again, etc. or at least that's how it looks at first.
The status quo at the end of this movie is basically the same as it was at the end of the TV series, give or take a bit of time-twisting emotional self-discovery en route. It's also a fairly lightweight storyline. It's not trying to compete with the TV show for gobsmacking twists and life-or-death developments. Instead, it's nice. It's gentle. It has some funny bits, then later some poignant ones. It threatens us with tragedy, but presented so lightly and gently that its resolution is slipped in with such delicacy as to be almost sleight-of-hand. You'll watch it, then say to yourself, "That was quite sweet," then probably never feel the need to watch it again.
One story problem I think it has, incidentally, is that it's a "will our heroes choose to act?" story. Personally, I don't think those work. Some are less unsuccessful than others, but I don't believe an audience ever really thinks that the answer could be "no". It's like Doctor Who stories that pretend to be dangling the possibility that the Doctor might retire from saving the universe. They're not. He won't. We know it. The best that can be achieved by those stories (and by this movie) is to get something worthwhile from the journey. We know its destination, but perhaps we can learn something about the characters from how they react to the process of getting there.
The film's first challenge is that it's set in a world-line with no time machines in it. Okarin unhappened them. It won't surprise you to learn that this statement will prove to have some loopholes in it, but it's still a step back from the most memorable, intense parts of the show.
Would it be a good idea to watch this before seeing the TV show? Absolutely not. Not only is it riddled with spoilers, but it's plugged into it so heavily that you wouldn't understand and/or understand the emotional significance of half the references. I'd suggest that this damages the show slightly with the reason why our heroes shouldn't act, which to some extent is taken on say-so instead of being shown dramatically.
There are more of those "eh?" Easter Eggs that I mentioned in the TV show, this time with a bloody flashback to a never-happened scene with the little girl Nae. It's a reference to the computer game, apparently, as is the Suzuha bad end. However we do at last get to understand the Empty World from the very first episode, so that's a plus.
I've been being mildly negative, but I did quite like the film. I like its Heisenberg-like model of timeline travel, which plugs into Okarin's Reading Steiner ability and ties in with real-life human observer physics. I'm fond of the characters and they're successfully used here, both for comedy and for more serious emotion. Also, more fundamentally, I like the film's confidence in telling such a simple, almost slight story. The World Without Spoiler in the third act is perhaps a little weak in its impact on the audience, but I don't think this ruins the film. It just makes it gentler and more elegaic.
At the end of the day, this is a film based on an anime TV series. These are almost never as good as the original. This one doesn't break that trend and I wouldn't recommend it for anyone who's not already a Steins;Gate fan, but there's a lot that's very good about it. Don't expect it to do everything the TV series did. Just think of it as a 26th episode and you should enjoy it just fine.