US citizen sent $60,000 to non US citizen relative in Vietnam through Western Union to help her buying property. The property is in her name. What is my tax obligation? What form do I need to file? Is this consider a gift? This is not a loan.

First no one would send 60,000 by Western Union, that would be insane, you do a bank transfer. It will also trigger 5 or more national security agencies that will investigate you and what the money is being used for.

I will say that this is a major investment there, what type of property is it ?
Next why would you have any tax obligation, you I would assume took this money out of your bank, where you already had paid tax on it. So where the money came from for you to send makes a different, If it was not a loan, and you were not paying them for services, then it is a gift.

There are other ways to send money to VN that will lower the transfer fee and all tax "obligation". Check the Vietnamese yellow page for CA ,TX , VA/DC , "chuyen tien"