Yep, this is indeed a traditional Taiwanese father. He's using money to try to control/manipulate you to follow the plan that he thinks is best. Welcome to the family!
If he's been polite and you feel accepted, then that's a good start. If he has the means to buy a house for his unmarried daughter and her boyfriend, and is willing to do so, then his heart is in the right place...according to Taiwanese culture.
But it doesn't matter if you're a foreigner or Taiwanese, I'd be extremely cautious of going down this road.
Have you considered marrying her? If yes, then remember that you'll have a relationship with in-laws to manage. For the rest of your lives. He's forcing you to show where you stand in the relationship. If you take the bait, then you'll forever be in the lowest position as far as face and status is concerned, because HE bought the house for you guys. You didn't do it on your own (or it wasn't YOUR family that paid for it which also gives you equal standing). Face and status might not matter to you, but it's a big deal to the guy you're playing poker with.
Also keep in mind that a daughter in a serious relationship with a foreigner poses a very legitimate flight risk. A 30-year mortgage (in her name) is the great way to ensure that she stays in Taiwan.
The best route, in my opinion, is for you to respectfully decline his offer. You can say that in your country it's normal for a man and woman to live together before marriage, but since this is Taiwan you respect his decision and won't live together before marriage. Just find a roommate if you need to save money.
(I'm not Asian but like pin2xbo I waited until after marriage before living together with my wife. It was a great decision and fun to get to know each other while setting up a home together. I was already in my early 30's so it depends on where you are in life...but agreed that after 2 years you should already have a good idea if you're compatible to live together, or not.)
I'm guessing that you're in your late 20's and still unsure as to whether or not you want to marry your gf. If this is the case, then the father has done a good job of helping you think about it.
If you're indeed uncertain then Plan B would be to communicate to the father that in your country it's normal for a man and a woman to live together, and that helps determine whether or not marriage occurs later on down the road. That at least lets him (and your gf, don't forget about her) know that you're thinking about marriage. Or at least pondering the idea.
Plan C would be to tell him that it's 2015 and this is just what couples do. No need to have any discussion about marriage. Not recommended because this will cause the most friction, but it is certainly one way to go.
Either way, all of those options let you maintain independence and give you man-to-man respect. You definitely don't want to be living under a roof that he helped pay for. But if you want to keep things positive then you need a graceful exit from the negotiation table because offering to help someone buy a house is a very generous offer. Just my 2 cents.