Dynamite Kid was considered one of the best workers in the business for about 5 years by that point. He made his name in Calgary and then really broke through in New Japan with his still legendary series of matches with Tiger Mask, which are considered classics and at least 20 years ahead of their time.
The Bulldogs were arguably the top working team in the world around '86, and were the only WWF act at that time that were also doing Japan tours while working for WWF. Vince didn't like that, but Dynamite wasn't going to give that up (he was the brains, Davey Boy was along for the ride).
So yeah, to answer your question, yes the Bulldogs were definitely a thing by then, and big international stars. Dynamite injured his back not long after the WMII match, effectively ending his career, and eventually sending him to a wheelchair by 40. He lives alone in England now, and is pretty much universally hated in wrestling circles because he was a terrible, miserable, selfish human being. Davey Boy obviously went on to a long, successful singles career, until he too injured his back in WCW when he took a bump on a trap door that was installed on the mat for a gimmick later in the show (one of the few Ultimate Warrior WCW appearances). Davey died a few years later, and many believe that the back injury sped up the process because he ended up back hooked on pain killers, but the reality is he was a guy with plenty of demons who abused steroids for decades, so his heart was likely to explode at some point anyway.
I do think it is fair to say that the WMII title win was probably the peak of the Bulldogs as an act. Dynamite got hurt, they dropped the titles to the Hart Foundation (in a match where Dynamite never tagged in because he couldn't walk), and Dynamite was never the same. They left in 1988, and did some random shots together (like the famous AWA match vs Rock & Roll Express which wasn't good but historical due to it being two iconic teams from the same era wrestling for the only time) until they split up, with Dynamite teaming with Davey's (kayfabe) brother Johnny Smith as the New British Bulldogs in Japan. Dynamite wrestled until he was literally crippled. His final match is incredibly sad to watch, from a human perspective of a guy who just couldn't let go because he didn't know how to do anything else and this was the only world he knew:
Read the YouTube description. His final match was opposite his biggest rival, Tiger Mask, some 13 years after they were having the best matches on the planet. Here, Dynamite can barely walk. Tiger Mask still wrestles to this day, and is still competent even pushing 60.