Dudes in recent years hitting each other hard isn't strong style. It was straight up just a buzzword Inoki came up with in the 70s to set himself apart. At most, it means using real techniques (as in strikes/submissions/holds/suplexes from various martial arts and Greco-Roman wrestling) to portray a real feeling match. It does not, and hasn't ever until very recently the term was perverted, meant just stiff the shyt out of each other the whole match. What Nak is doing in WWE is closer to the original Inoki strong style than what Ishii and Shibata are doing giving themselves brain damage every match to make people think they're tough guys.
Dudes in modern day NJPW are stiffing each other more than shoot style dudes were doing in the 80s and 90 (the actual, legitimate progression of Inoki strong style) that was supposed to be like 90% shoot besides the finish of each match.