Of course they'd want to date fictional characters. One, they're drawn to be beautiful (well, mostly, and I commend those artists who draw more realistic depictions of women); two, because of having played the game/watched the show, they've gotten to know the character intimately WAY faster than dating a real person; and three, many characters have excessive amounts of personality which attracts men, and is great for the screen, but wouldn't be as appealing in real life situations. Getting attached to characters is fine and well and it's part of what makes entertainment, well, entertaining, it just becomes problematic when some cannot accept both the fictional world and the real world the way they are, and become consumed by fantasy...
In any case, I think the real question is would the game characters want to date them? 😛