The MKR1000 is basically an Arduino Zero with a wifi shield piggy-backed. It is capable of TCP/UDP, both P2P and AP mode should be possible.
Just from the datasheet for the MKR1000 I would suggest you also take a look at the ESP8266MOD (ESP12F). This little thing is fast! It comes with 4Mb flash memory and there is good integration with the Arduino IDE (need to load additional board info first).
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Lewis