Not really it cannot be used for gaming because of the high cost of data to use. Smartphone's seem to hit a wall in most apps ,with user payments and privacy. It still has a way to go before it replaces the humble PC.
There are single-player games for phones, you know. Even ports of older PC games. Not to mention that 'computer' does NOT mean 'games machine'.
Smartphones do everything a computer can do, albeit to varying levels of quality due to screen-size, storage limitations, data connectivity or other constraints. This means the functionality is there but there may be tradeoffs or the experience may be different/restricted.
Can you name a function of a computer that can't be performed on a smartphone?
Can it send and receive email? Tick.
Can it browse the internet? Tick
Can it be used as an entertainment device? Tick
Can you print from it? Sure (with the right phone and printer)
Can it do word processing? Tick
Can it do photo editing? Tick
Can you install other operating systems? Tick (Well custom ROMS for android phones)
Can you install other programs/apps? Tick
Can you videoconference? Tick
Can you connect external devices and/or storage? Tick
Plus you can make calls, send SMS etc etc.