Yes, a child can be the 'continuation' of the father after he has passed away, but it takes more than just sperm to make a baby. Two sets of chromosomes are in that child, the child could be a mirror image of the mother, in both physical aspects, as well as 'mental qualities and traits'. So no matter how much the father (and perhaps mother) want and expect the child to be a replica of his father, in culture, tradition, mindset, etc. he/she will still be affected by his mother, even moreso than they would by the father i would say, since the mother is the main person who raises the child.
So yeah, what was said in those two links doesn't cite any islamic evidence or sources, it's merely the opinion of whoever wrote it. I'm not saying that it is wrong for a person to take after their father, if the mother wants that, then so be it, but by no means is it "islamically" right that that happen.
Again, maybe we're just disagreeing because we had different ideas of "lineage". Like I said before, lineage =/= cultures and traditions, for me anyway.