I think you ask a great question because funnily enough when the 'new' World Grand Prix was created in 2015 I seem to remember talking to a mate at the same time about this very topic
My view is this - over the years a lot of tournaments go through many venue changes, formats, sponsors, trophies and broadcasters - so there's a fair few tournaments out there where the current edition may be a bit of a complete contrast to the first edition of the theoretical continuous tournament.
As in the case of the Grand Prix, I think most would agree that from 1982 until 2010 it was one long continuous tournament - and the two things that I feel kept it as so were the broadcaster (BBC for every edition) and its 'slot' in the calendar (seem to remember it was always around October). In edition every time the format changed or the sponsor changed or the name changed, it was no doubt it was a change rather than a 'replacement'.
In 2010 Barry Hearn decided to rename it to the 'World Open' with a change of format (which in all honesty I feel was a bit of a poor decision, best-of-5s!!) and this was the last edition shown on the BBC. It used the same trophy and was held in the same city as previous years.
When the move to China was announced, it was definitely a 'move' rather than a new replacement tournament as it was phrased that way. But it therefore had a change of country, venue, trophy (Mark Allen lifted a brand new trophy), format, broadcaster and sponsor. I therefore do ask myself whether it really has anything to do with the BBC Grand Prix from 1982-2010. My opinion is that it doesn't.
When they introduced the new 'World Grand Prix' in 2015, Hearn marketed it as a completely brand new event - featuring a unique format (at the time) of the top 32 on the 1 year list. Now at this time in 2015, the World Open had effectively been dropped from the calendar - its 3 year stint in China came to an abrupt stop with disagreements with the venue. So I think that's maybe what kind of prompted some to feel it was a continuation of the World Open, more so because they used the same trophy (which hadn't been in use since Neil lifted it in 2010).
But soon after the World Open was re-established once again in 2016 in yet a completely new different venue in China (Wushan) with yet again a different trophy to the one Allen lifted twice in Haikou ..
So to conclude in my opinion, the current World Open in Yushan I feel became almost a brand new tournament in 2016 (or 2012 at the earliest) and has the most weakest irrelevant connection to the old BBC Grand Prix from 1984-2010, though there is still the most slightest of connections.
The new 'World Grand Prix' using the same trophy as the old BBC Grand Prix I think is just, as someone else mentioned, a bit of a 'gimmick' or a 'quirk' - odd in a sense that Neil lifted the trophy last month for the 'first time' - but in another sense certainly didn't.
I doubt the trophy has a plaque on it with the BBC Grand Prix winners engraved, let's put it that way (though I think it did when Judd won it in the inaugural year in 2015?!)
But then again the Yushan World Open trophy definitely does not have the BBC Grand Prix winners engraved on it either..
It's all a bit strange not going to lie but going back to what I said at the start - tournaments change so much over the years to the point where a lot of them you simply can't really say it's been one long continuous tournament from the start, even if Wikipedia says otherwise.