It seems like something an edgy fan would make up, or perhaps something someone against violence in video games would spread around to tarnish the games reputation. Snopes lists the rumor as debunked, likely the result of someone looking to blame video games for the tragedy, or someone looking to scare others.
Eric Harris did have an affinity for the internet, creating and sharing multiple doom mods to the internet, some of which are still around today. There's a decades old Urban Legend that Eric Harris and Dylan Klebold, the infamous Columbine Killers, created a modded DOOM map to resemble parts of their school, to ”train” on it.