But if this new guy becomes Another Zi-O, why hasn't time changed for Sougo to remove his memory and powers? Or are we just throwing that concept out the window now?
I think that's what they're aiming for, but if that's the case why did Oma Zi-O act as if seeing his younger self when Decade sent Sougo to the future?
To answer your second question first, some reasons could apply. The fake Sougo from the future (assuming it is a fake) could have been pretending to be Sougo to mess with his head or to ensure the future in his favor. Decade was the one who sent Sougo to the future, so there's still the possibility that it's an alternate dimension Sougo saw and not the same future Geiz & Tsukuyomi are from. The Time Jackers are trying to dethrone Sougo and make someone else the king; and if the timelines are currently unstable with multiple possible futures, then who knows for sure what future holds.
As for your question about Sougo not losing his memories and powers...
There is a lot of possible answers. I waited til the episode after this to find out for sure, but didn't get any. So I'll list the three most likely answers...
- Zi-O, Geiz, and Tsukuyomi are using gear made for time travel. It wouldn't be effective gear if it didn't make them immune to timeline changes, paradoxes, etc. I imagine this is the most likely answer, and I've contemplated this as a possible plot point since the beginning of the show.
- Ever since gaining the power of Zi-O II, not only can Sougo predict the immediate future, his subconscious is manipulating how the future plays out. Sougo has more power than he realizes, so that might be keeping him from feeling any ill-effects from Another Zi-O's appearance.
- The Day of Oma is drawing closer, and Regulus is possibly making Zi-O more powerful as the day draws near. Possible timelines are converging on this day, and we currently have 3 possible champions that could become the new king/savior. If time hinges on this event, then that might be a fail-safe that is keeping Sougo from having his own timeline changed because of Another Zi-O. In other words, can't have Day of Oma without Sougo and his Kamen Rider powers.
But that's just me giving the writers the benefit of the doubt. There might even be a simple answer; like the creators forgot about/discarded that history wiping aspect. Maybe they have jumped the shark and are just doing whatever they want now. Maybe answers will be revealed even further down the line. I've just been impressed with the writing of the show so far, it's hard for me to believe that they'd change creative direction for no reason, but it's possible. When I saw the first few episodes of Zi-O, I had to use time travel tropes and other related pieces of logic to try and explain the confusing parts of the show, details that were never fully explained in-show. But it's always possible that the show runners are just doing whatever they please, and most of the good writing is coincidence. ¯\_(ツ)_/¯