The interview is clearly a mistake, but it happened.
Hopefully under-the-radar measures will be taken to try and discreetly counsel Mr. Markle that he's being taken advantage of, and his speaking out is only hurting his image and hurting Meghan and Harry, instead of solving anything for anyone. Under normal circumstances, people who speak out in this manner are ostracized by the royals. This is a delicate situation because Meghan loves her father and he clearly loves her and respects and admires her new family, which he said many times during the interview. Still, all along M&H have probably been handling interactions with Mr. Markle carefully, especially knowing that the half siblings are in contact with him and may be influencing some of his poor decisions.
It should be quite obvious to anyone who actually listens to the interview that it was designed to 'get' Mr. Markle in any indiscretion they could capture. All the while, the hosts were at the same time trying to stroke Mr. Markle and bamboozle him with feigned praise.
The 'gotcha' parts of the interview are obviously being played up in the media, rather than the harmless and more interesting parts of the interview, including the love he feels for his daughter; the nickname he had for her during her childhood; the previously unseen family photos that were shown; how Meghan was helping her Dad prepare for the wedding; the chronology of his heart ailment interfering with the wedding plans; his tweaking reference to Markle family members 'coming out of the woodwork'; his love and respect for Doria and a reference to work being part of the reason why their marriage broke up; how he feels that Meghan has always been a princess; his reference as to why Meghan didn't invite any Markles being because of the clamoring by so many of them, which made Meghan feel the need to proceed with caution: thus, that's the reason she decided not to invite certain Markles she may have been planning to invite -- probably Ashleigh Hale was one who would have been invited.
Overall, we can see why the royals 'never complain, never explain,' and rarely mutter anything but pleasantries in public, aside from advocating for charitable causes, trying to be cautiously self-reflective now and again in the interest of being open and trying to help others, as well as making the odd humorous remark now and again. They can never win with this level of OTT attention and the 'gotcha' mentality of the ever more rampant and uncontrollable tabloids, which in many respects extends to mainstream media, royal reporters, and royal followers.
Prince Philip of course is a different story. He's always carried himself to the beat of a different drummer. But he's also known how to play the game within the lines. The Queen clearly has always respected his independence if not always his outspoken gruffness. In the case of Mr. Markle, I doubt anything will be said by BP or KP. I do hope Mr. Markle can somehow be helped to learn how to stop talking. But it occurs to me that Meghan may have always found it difficult to manage or predict the outcome of Markle family conflict.
ETA:
I agree with your take on the exchange of money
@Osipi. Mr. Markle likely rarely agrees to accept money from his daughter. Yet ironically, it may be that he doesn't realize how taking money from these tabloids is harmful to his image, as it's rightly seen by many as trading off on his daughter's royal connections.