Probably. I mean, presuming that they found touch DNA. I do not believe this killer cut himself and dripped blood anywhere. I do not believe he stepped in much blood, either - but if he had, his footprints might still yield some of his own DNA (from the soles of his feet, as we all walk around our own houses and get human dust on our feet). However, separating out the perp DNA might not result in a complete (23 pair) sample.
So they'd vacuum the house with special vacuum cleaners. The protocol for this listed in most forensic books is to use a special vacuum on the bodies of the victims, then on their bedding, then another bag for the room in general, and then of course, the stairs we know he used. Take swabs from that sliding glass door (he was probably gloved - very little DNA left).
They might even look at air filters (from the heating system). There are about 3 billion base pairs in the human genome. Many are shared among us, some have extremely diverse expression (that's what you want to find, so you can separate out the DNA). For example, nearly all of us have the same or similar allele for having 5 fingers on each hand. The 5 bones in a dolphin's fin come from a related but distinctive allele - but ours is quite similar to the one possessed by chimps. Nearly all of us have a very similar allele at that spot, doesn't help much in identifying.
So after the DNA is carefully reconstructed (the various alleles are marked off from each other with a unique punctuation-like set of codes), the investigators can go to specific places in the genes (if available) and start to see what individual markers this person has. There are lots of different ways to do this, and different subspecialties within this field of study.
But what if there is no complete sample of this person? What if it's only partial? Much can still be learned forensically, but it might not lead quickly to one specific person.
I would hope that they find the Y chromosome of this person, because that would place the person within a particular historic/ethnic group, more or less, and that could help the investigators decide which portions of the perp's gene map are most important to look at. Let's say he's R1A1b (a common Y chromosome in European men - mostly northern European men for that one). I'd then want to know the alleles for eye color, hair color, and several others (on different chromosomes - and those chromosomes are likely no longer linked together by the structure of a living cell...)
If instead, he's Q or R1b1 (like the men in my father's family), then those bits of information give a different overall ethnic/historic profile. Just that bit of information could help investigators narrow down a set of POI's.