I was a little curious about the "protocol" (?) of how cases are sent to higher courts for appeals. For example is there a different path for a case like this.
I actually just took a class on this topic and got an A, so hopefully I can clarify some. There are two ways to get a case to SCOTUS, either by filing in Federal court at the district or specialty court level (Bankruptcy, Tax, etc.) or by going through the state courts. State courts are the workhorses for most litigation. Federal district courts are courts of "limited jurisdiction" and generally only take cases if there's a question of Federal law or there's a dispute between two parties from different states and the claim is over $75,000. So this case, assuming it's a wrongful death/products liability, of high value, and there's exactly one NY plaintiff and one OH defendant (I can't read the article, subscription req'd), could in theory go to Federal court.
From the trial court level, which in state court for example would be say a Mass superior court or Mass district court, or in a Federal case a Federal district court, if there's a preserved appeal, a party can appeal to an appellate court either by right or by writ of certiorari. An appeal by right is not discretionary and the appellate court must take the case. For example, Texas has a Court of Criminal Appeals that specializes in criminal cases that are appeals by right. In contrast, an appeal filed by a writ of cert is discretionary and the appellate court may or may not take the case. This kind of case would be appealed by a discretionary appeal.
From a litigator's standpoint, whether or not to file a discretionary appeal should be influenced by the "standard of review." There's three basic ones with variations:
de novo, which means the appellate court gives no deference to the lower court's findings; clear error, when the appellate court should only reverse if the trial court was blatantly wrong on a point; and abuse of discretion, when the appellate court is highly deferential to the lower court and should not reverse unless there's something egregious. Standards of review are a complex topic.
After the initial layer of appellate courts, which in Mass and NY would be the intermediate appellate court (Mass Appeals Court), or in the Federal system the circuit courts (1st Circuit), there's either a second layer of appellate courts (NY Court of Appeals; Mass SJC; en banc hearing in a circuit) or it's time to petition to SCOTUS. For example, in NH or RI, someone's case could go from the state superior court --> state supreme court --> SCOTUS. In contrast, a Mass case or this case in this thread could go from the state trial court --> state intermediate appellate court --> state supreme court --> SCOTUS. In Federal cases, it would probably go Federal district court --> Federal circuit court --> en banc circuit --> SCOTUS.
IANAL and feel free to do your own reading.