"Are you purchasing this firearm for someone else".
No, what it asks is "Are you the actual buyer of the firearm(s) on this form?" which is very different from what you stated. Buying a handgun, with your own money, to give as a gift is NOT against the law, nor is it an example of a "straw man" purchase. The OP said "giving," not "buying with his money." If he is buying with the foreigner's money, then this is illegal.
The second part is, is he (the Philippine national) legally able to own a firearm in this country (the US)? This varies based on immigration status. If he is not, then you are breaking the law in transferring it to him here well before it ever starts to go over seas.
I have looked into transferring firearms out of the country before - but only Mexico and Canada. It can be done, but you really need a customs agent or FFL who is well-versed in it and knows the hoops. As to the Philippines, I'm sure you can track someone down who knows that. I'd expect to pay $150 to $200 for the shipping and customs processing, if it legal at all in the Philippines. I know nothing of their firearms laws. If the Philippines allows nationals to import handguns w/o restriction, it could be as simple as declaring it as checked baggage at the airport, nothing more.
So, break the whole problem down into three parts:
1) Is it legal to purchase a handgun and give it to him?
Yes, IF:
2) He is legally allowed to own it in the US based on his status; and
3) What are the Philippines' laws on a national importing a handgun?
Hope that helps.