Huh?
"Grav waves and dark matter have an effect on gravity..."
Dark matter has an effect on gravity, gravitational waves are a change or variation in/of gravity. Saying that gravity waves have an effect on gravity is like saying a change in something creates that change.
"...and thus time, variations of which..."
There are not different varieties of time. Variations can occur in time, but it's all the same sort of time.
"As you'd expect, if two of these clocks were placed at different altitudes near the Earth's surface, the higher one would tick slightly faster than the lower one, due to classic time dilatation."
There're two types of time dilation: gravitational, where the local rate of time is affected by mass, and relativistic, where the local rate of time is affected by spatial motion; there is no "classic" variety.
"...an effect sometimes called the gravitational redshift."
Only people who don't know what they're talking about would call gravitational time dilation "gravitational redshift": time dilation and 'red-shift' are two entirely different phenomena.
And no, I don't think I'm just being pedantic - these mistakes, far from informing people, just mislead them.