My immediate reaction is to say no. But …
… some reboots are successful. They fall into two categories:
1. Shows that take the original premise, update it for modern tastes, and do something new and interesting with it. Battlestar Galactica is an example of this. They ran with the original idea (a desperate survivor fleet of ships, fleeing robotic pursuers, seeking some distant salvation) and turned it from flashy Hollywood kitsch into gritty survival drama.
2. Shows that could arguably stand on their own but get a boost from taking on the show and character names of the original, while really creating a new show that could have run just by itself. Hawaii 5-0 is the current example here; it bears next to no resemblance other than names and setting to the original, but it has survived several seasons on what it’s been able to do as an entertaining story.
(H50 could have been called The Hawaiian Beat, with lead characters named Joe Smith and Bob Brown, and told exactly the same story. There’s nothing about the show that is intrinsically the same as the Jack Lord version. But wearing the H50 names arguably gave it the initial boost to get people watching and thus get hooked. I might roll my eyes at the tactic, but it worked.)
[Neither of the above necessarily encompass all my feelings about either show. But my own personal caveats aside, both were successful.]
Either approach is respectable. Doing something new and exciting with traditional characters is an old tradition dating back to the first time someone told news stories about the gods and heroes of an old myth. Hell, 90% of Shakespeare falls under that category. Doing something new that you just slap the old name onto but still make a successful tale about also has a long tradition.
Reboots that tend to fail are the ones that try to recapture the lightning — making a show that is “just like” the original but with new actors, a possible new setting, but no new vision. A lot of TV reboots that start with “The New …” fall into this category, and they almost universally fail, because people want continuity but not an attempt to be identical. Not only is the latter impossible, but it’s boring.
The Magnum, P.I. plot that’s described in the story sounds like an interesting twist to the original per Type 1:
The new Magnum is described as an update of the original. It follows Thomas Magnum (Selleck’s former role), a decorated ex-Navy SEAL (also like the original) who, upon returning home from Afghanistan, repurposes his military skills to become a private investigator. With help from fellow vets Theodore “TC” Calvin and Orville “Rick” Wright, as well as that of disavowed former MI:6 agent Juliet Higgins, Magnum takes on the cases no one else will, helping those who have no one else to turn to. Action, adventure and comedy aside, Magnum P.I. will also explore a brotherhood forged by the trauma of combat, what it means to return home an ex-soldier, and a commitment to continuing to serve while in the private sector.
It feels more straight drama than the dramedy as the original was. The Sellick Magnum had its very serious moments (esp. as the series progressed), but it was at its core a light-hearted detective romp. Playing some of those same themes straight might well work out very well.
Or it might be a hot mess. Who knows until they do it?
The original Magnum, P.I. ended in 1988. Thirty years is not a bad interval to look at a way to do something fresh with the idea of a war vet returning to Hawaii to become a private investigator. I’m willing to see what new they have to say.
I look at reboots now like I look at the Hardy Boys (and presumably Nancy Drew) books. They're rewritten every so often to keep the same age group reading them. Though it makes us older watchers feel older when we think we can relate but, really we're still watching Tom Selleck in our heads…