These particular lineplots are called parallel coordinate plots.
I think what distinguishes a true slopegraph from a parallel coordinate plot is that in the former y-axis remains the same variable and scale. On the other hand, many of the "almost" examples from that link are really parallel coordinate plots.
I agree. I've appreciated them (lineplots, slope graphs, or "bumps charts") since Kaiser Fung redrew an Economist chart of birth ratios in Indian states:
Here's a resource for creating them in Excel:
Ben Fry’s Baseball Chart looks more like an art-museum-security-laser plot. Or, maybe that's the 'no association' condition.