Anyone who says that this is or is not a valid claim misses the point and is relying too much on marketing materials they have read.
Presumably OP was delayed by 4+ hours into EWR and is thus, unless "extraordinary circumstances" existed, entitled to compensation of EUR 600 because this was a departure by a non-EU carrier, but from the EU.
Whether the cancellation is an "extraordinary circumstance" due to an "extraordinary circumstance" on the preceding rotation, e.g. EWR-MAN, is a matter of factual proof. By way of example, if this was BA at LHR, it would be highly unlikely that BA could reasonably argue that it could not rustle up a backup aircraft and crew or reroute passengers, given that LHR is its worldwide center of operations.
But, this is not the case at MAN. Where was the closest relief aircraft and crew? If this matter is litigated, it will be UA's burden to prove these facts. That won't be too hard for UA to show in this case. But, it does not mean that you will lose if you ultimately do litigate as this is a claim which UA will likely defend because it goes to a core issue.
If you make a claim, see what happens. You can then decide whether you want to litigate or not. You can also check one of the claims agencies. They will eat 25-33% of the compensation as a fee, but can be a good indicator because they only take cases they can win.