It's important to remember that this is the series that first described time as a big ball of wibbly-wobbly, timey-wimey... stuff.
One way to reckon time would be as a big stack of Gallifreyan personal timelines. This "line" began with the birth of the first Gallifreyan, and continued strictly along the way he (she?) experienced time. Whatever time travelling she did is irrelevant: her moment-to-moment experience is always moving "forward," no matter where those moments might have taken place in "objective" time.
Eventually, this Gallifreyan had children, and when this happened, their own personal timelines began. You could view these timelines like a deck of cards, stacked on top of hers but shifted forward slightly (the time "behind" them being the time before they were born). These children's timelines worked more or less the same way hers did, and when hers died out, theirs continued. They also had children, whose timelines continued to move forward from their own perspective.
As you stack these cards, you start to get something that looks like a leaning tower, and you could see the direction that this tower leans as one way to reckon time. By this reckoning, The Doctor's card juts out further forward than any of the others. He has experienced the cutting-off (the end of experience, i.e. "death") of every other timeline of every other Gallifreyan who lived while he was alive, and as we go forward in his own timeline, no new Gallifreyans can be born.
So in this sense, The Doctor is indeed the last of the Time Lords. His card is the furthest forward in the stack, and at the point he is experiencing, there are no other cards left. It's a very Gallifreyan-centric way of looking at things, being defined solely by the experiences of Gallifreyans, but The Doctor is Gallifreyan, so it makes some sense that he would see things this way.