If you're comfortable with the reasons for alternative pipe construction I won't reiterate them.
Yes you're missing something, but it's not cryptographic. It's just that informative artwork and graphic design is not the usual cryptographer's skill set. So they bodge it as best they can. So single lines can represent many things. Sometimes they can mean a standard MD width of interim hash passing through, and sometimes they represent twice the width. The feature that gives it away is the finalisation function /output compression function. If one of these exists, it suggests (graphically) that the interim hash width exceeds the input /output block widths and has to be reduced.
I understand your confusion. Figure 3 of your The Wide-Pipe Hash: A Modified MD Hash seems to show yet another alternative type of wide pipe that you might call staggered. This is my nomenclature for it as it's not specifically named, but I wouldn't call it standard wide pipe. It seems to show iterated compression functions of input width IV + message and IV width output. It's almost the fast wide pipe compression function mirrored.
The designers randomly try all sorts of weird stuff in order to improve the security of the total hash. It's called incremental development and that's how things evolve. So some of your examples are slightly different in form. They just sometimes draw /explain it very badly but then they're not graphical artists. Your wiki example doesn't name the wide pipe hash, so we don't know what the compression function is. It is entirely possible that it keeps IV compression and message block compression entirely separate until finalisation. But it's a clip art style image and not very detailed. Between subtle variations on which bit is wider than the output block width and bad drawing, it's hard to figure it out.