This game is also known as Hot Shots Golf in the USA and Minna no Golf in Japan (often abbreviated MinGol on Western sites).
E.G. at first glance appears to be a simplistic cartoon styled Golf game. The characters are heavily stylized and anime inspired, the courses are fictional and have wildlife on the fairways and major obstacles (buildings for example) in the direct path to the hole. It would be easy after a couple of minutes play to conclude this was not a deep Golfing game.
However, spend a bit more time and you begin to see that underneath the cutesy exterior there is a much deeper gaming experience. The actual golf mechanics are simple enough using timed button presses to set shot power and hook/slice. There are then additional controls to induce spin in various directions and special shots which are limited in number, that can be used to gain an edge - it's in these extra abilities where the game becomes serious if you want to attain the best scores.
You start as a novice golfer. In order to progress to Intermediate and higher levels, you complete golfing challenges which, in the Single Player element involve playing rounds of golf and gaining points through doing so. Points are awarded on a shot by shot and hole by hole basis. A good drive for example nets some points, ending up in the rough gets less or no points. The challenges start off easy - 9 holes against a weak set of computer players. As you get deeper into the game the challenges take on greater difficulty and new rules are introduced (+2 for landing in a bunker for example, or extremely strong winds).
Progression unlocks new characters, courses, clubs, balls, clothing, music and other items - there is a significant collection game available in here if that's your thing. Some of the items are just cosmetic but others like balls, clubs and even the characters themselves change your game. Unlocking an item is only the first step though, you then need to buy the item using your accumulated in game points to actually use it on the course. This creates a nice tension about how you spend your points to best approach the future challenges (unlock a new character, or stick with what you have and get clubs and balls for example).
The Single Player alone is probably 15 or 20 hours worth of gameplay to unlock all the courses characters and major options for clubs, balls and other game changing options. To get clothing and other cosmetic items will potentially take longer.
All that is without looking at where the other 50% of the gameplay value lies - the multiplayer. Multiplayer tournaments in EG are fast paced affairs with 30 players per tournament playing asynchronously (that is to say, you don't see the other players while you are completing the hole, rather you all rendezvous at the end of the hole to chat).
The main online mode offers a lobby system which is a mini game in its own right. You create and customise an avatar which is reminiscient of a bobble head and enter the online lobby where you can walk around and interact with the environment and other players. Tournaments are listed by their start time, so you register for an upcoming tournament and shoot the breeze with others in the lobby until the start. Tournaments have various restrictions just like the Single player.
Don't be fooled by the cute nature of the lobby here either, the Multiplayer is cut-throat and you'll have to be extremely proficient at the game and efficient in getting birdies and eagles to win.
The multiplayer also has a ranking system and the best players are able to enter the top rated tournaments thus creating a league feel to multiplayer.
So the game is deep, there's a lot to get your teeth into and assuming you like Golf and multiplayer the game has almost endless replay value.
There are some downsides though. The main problem are the graphics. The game looks nice enough but it is rendered at less than the resolution of teh Vita's display. This means the game appears somewhat "soft". Additionally there are some jagged edges present - mainly on things like shadows - that are jarring. Your character looks good though and is nicely animated, but the wildlife on the course is rather robotic.
So graphics aren't great - for context, this is compared to other Vita titles. This game still looks and performs better than any on smart phone, tablet or other handheld gaming device.