This is the best single-player indie game ever (next to Nidhogg which is the best multi-player indie with online play game ever.)
You play as Georgio Manos, the world's first revolving limousine driver. What's a revolving limosine? Well, it spins. Constantly. Clockwise, most of the time.
Your vehicle is constantly rotating, you simply navigate by pushing the stick in any direction, you can speed up your movements and your rotation by holding a shoulder button/trigger (Vita/PS4 respectively) and you can use Upgrades with Square, these cover a wide range including slow-mo, one that extends your combo time, one that lets you change your rotation on demand (normally you have to bounce off of these blue springs/pylons to do this.)
In terms of style, the game is like a mix of Crazy Taxi and GTA1-2. It's got a top-down perspective, plenty of destruction and civilian roadkill. It's also got a sandboxy map with plenty of hidden collectibles (cash, different horns, properties to buy to make more money over time, Sick Jumps, etc.) but you unlock missions one-by-one by completing the previous. Occasionally bonus missions/mini-games appear that involve bouncing a ball on top of your limo, or running over lots of pedestrians in a certain amount of time (don't worry, they're the Endangered Animal Hunting Committee!)
The missions are all accompanied by WONDROUS 70s B-movie live-action cutscenes. The game instantly reminded me of Twisted Pixel's games ('Splosion Man, Comic Jumper, The Gunstringer) and I just read that the developers, No Goblin, were founded by Dan Teasdale, one of the big names behind Twisted Pixel. That also explains the voice-over cameos by LPers such as Medibot who plays Jeffrey the Skeleton, and PsychedelicEyeball who plays the game's overly-French antagonist. Medibot as well as the rest of Pokecapn's Posse provided an in-game commentary track for The Gunstringer as the team liked their Sonic 06 LP (other popular LP groups such as Achievement Hunter/Rooster Teeth also had commentary tracks.) Another amusing fact is that Georgio is a silent protagonist, even though she's a real person.
Unfortunately, much like 'Splosion Man (and ironically this, in addition to the live action stuff, is what made me look up the Twisted Pixel connection,) there are some minor problems. Considering that both games feature really strict time trials (or maybe 'SM's were easy and I was just challenging myself,) it's not good design that spawns are random. In 'Splosion Man, your primary method of speeding around and jumping higher was by blowing up enemies, but they would appear in random locations within a certain range (or at the very least they spawned facing a random direction and their walk cycle would change their position different depending on how long it took you to get there.) This made speedrunning completely inconsistent, and incredibly frustrating. In Roundabout, you can quickly retry a mission, but you spawn in the same orientation you were in before selecting retry (or it's random, but I'm confident that it's the former.) This can cause you to sometimes bump into something right away, or not be in the correct position to fit between the first set of obstacles in front of you. Considering that you can only take 4 hits before the 5th hit detonates you, and most missions don't give you a timely route through a garage, this is incredibly frustrating and will cause you to restart runs mere seconds into them, but not a deal-breaker.
There are some nifty extras that you can turn on at any time, classic-style cheats like big head mode or a mode that replaces all sound effects with fart noises...You can also trick out your limo with hats, the collectible horns I mentioned before, and paint jobs. There are more references here like a Japanese hot dog octopus hat named Octopus Dad, a paint job named after GE-OP (another LPer,) and a paint job called The Hideo that looks like a cardboard box (there are stickers on it that look like the Konami logo, which feels kinda tasteless but the game came out on Steam months before Konami lost their minds.)
So yeah, the game is on PS4 and Vita now, WITH CROSS-BUY (but no cross-saving as far as I know,) as well as Steam, for 14.99. It's awkward and hilarious and super addicting, I intended to play it for maybe 30 minutes last night but ended up playing it for 3-4 hours.
Here's a video that I remember being pretty amusing, but I also remember the player not really getting the humour so it's not the best:
Dr Pepper. It's an intellectual drink, for the chosen ones.