As an open-world game set in a vast, dry, wasteland, Mad Max doesn't thread any new ground. It's mechanics are firmly set in other game's. Combat, for example, is lifted almost directly from the Arkham games. But even if there's nothing new, everything is implemented with attention to detail and cohesively put together into a polished whole.

Most of the game is fast-paced car combat. You can crash into enemies, shoot out their wheels and use a grappling hook peel off their armour or to snatch the driver from his seat. There's plenty of driving to do thanks to the expansive desert, but also lots of small chores that keep you occupied. Yes, they could be characterised as "busy-work" but they are sufficiently varied that I didn't get bored.
This is thanks to the fact that no two locations are alike. From the layout of the four main Strongholds to the small scavenging locations with no story purpose whatsoever, every single place is unique.
You've got big crazy structures made up of crashed planes, Repurposed sunken boats made into small shelters, multilevel bases stuck in the middle of the ruins of a bridge. Some of them even tell small personal stories or give character to the wasteland. Imagine a game filled with hundreds of small locations as interesting as Fallout 3's Megaton and you get the idea.

There's a fast-travel system, but it's not just the usual "go to a place and now you can automatically fast-travel to it". It's much more deliberate. There's a whole rigmarole that forces you to access a balloon, go up into the air and surveying the field with your binoculars. Not only it adds variety and immersion to the world, but it also servers as a much-needed respite from the frenetic driving and killing. Up there in the balloon the wasteland seems almost peaceful, and you can stand there for as long as you want, relaxing, taking it all in. Everything sounds muted, the sounds of the wasteland feel distant.

This impecable sound design also helps to create a more immersive experience. Depending on where you are, you can hear character's shouts echo in the surrounding cliffs. Far away car noises alert you that a war-party is approaching, and during ground combat. Each area of the game sounds different.
And being a meteorologist, I cannot help to mention the wonderful skies. Not many games pay so much attention to a feature that covers half of the screen. Mad Max's sky is dynamic, ever changing, beautiful and BIG. Clouds feel volumetric and change colours as the day goes by. I could be trying to take down a caravan at top speed with multiple cars ramming mine from the sides and suddenly look up and be amazed.
The one mechanic that is an absolute zero and, should it be complete excised from the game would not be missed at all, is the minefields. The less spoken about that horrible design decision, the better, but let's just say that it is boring, annoying, completely nonsensical chore.
Now, if I've just spent more than 400 words talking about the game without touching on the story is because, similarly to Fury Road, story and characters are mostly hinted at. What little characterisation there is, though, is hit-or-miss.
The big breakaway character is Max's sidekick and blackfinger, Chumbucket. This deranged hunchback is one of the most mad-maxy character of the whole game. Both his mind and body, twisted by the decrepit wasteland, contrasts with the relatively normal-looking models and normal-sounding speech of the rest of the cast. He is also kind of endearing and superbly useful and knowledgeable.
In fact, even though Max drives the car, it is Chumbucket who drives the narrative. He is the one telling Max where to go and who to meet, and most of the time he is the one doing the talking. He even nags Max to get on with the main mission when he spends too much time fooling around doing side-tasks. In those moments, Max is less of a protagonist and more of Chumbucket's personal driver.
On the other hand, Max himself is a bit of a wash. Even though Max can speak and does at times, he's almost a silent protagonist. We get no backstory (although people who saw the first movie know it pretty well) and his only stated goal is to go to the Plains of Silence, where he thinks he'll find respite from his demons. To that end, he will use and abuse whoever gets on his way. Which raises two problems.
The first problem is that Max's cynical and egotistical attitude is not consistent with the player's actions and most of the mechanics of the game. During your journey, you will help multiple communities grow and rescue people for little if any material gain to Max. The fact that you can destroy enemy bases which then ate taken over by your "allies" who will periodically give you scrap (the game's currency) makes absolutely no sense for a character that doesn't do "allies".
Fortunately, the minimalistic nature of the narrative makes this a non-issue; at least until the very end, when story missions start to get very story-heavy and the second problem arises. When Max's use and abuse of people in service of his self-absorbed path of self-destruction takes front stage you realise that you are actually playing the bad guy, which is not a comfortable situation to be in as a player.
Mad Max is the uncommon move tie-in that is actually very good and holds up as a stand alone adventure. This is probably due to the fact that it merely takes inspiration from the movies instead of being an adaptation, and it's thorough attention to detail.