Does the Message Integrity Check in WPA(2) standard solve the problem of non-repudiation? Whether the receiver can be sure that the message is sent by the source only and not spoofed by someone else?
No it doesn't. 

Message Authentication Codes (MACs, which in networking some may call MIC in order to differenciate from Media Access Control) are symmetric-key primitives that only provides authenticity and integrity of the message exchange. Non-repudiation requires public-key cryptography.