So here it is Kamen Rider Zi-O's Shinji Kido wasn't Kamen Rider Ryuki? Not able to make sense? Ok. Let me tell you that this reason it directly linked to why it was Another Ryuga & not Another Ryuki to appear in Zi-O TV Series.
So everything connect to the final episode of Kamen Rider Ryuki. Everyone might have the memory of Shinji Kido & Ren Akiyama being the Kamen Rider Ryuki & the Kamen Rider Knight but I guess you might have forgotten what had happened in the end.
Many might have thought that Shinji's Kamen Rider Ryuki was erased from the history just because Another Ryuga had appeared. But it's not true. We were mislead.
The world was reset and Shinji & other people who had died were still alive. So in other words they never transformed into Kamen Rider. Kamen Rider Ryuki didn't exist according to TV Series' New Timeline.
When it comes to Asakura, I am not sure how to explain this. He was alive after the reset but considered dead in Kamen Rider Brave Spin-off. But for now, RIDER TIME: Kamen Rider Ryuki / Kamen Rider Zi-O is following correct timeline.
Wait! If Kamen Rider Ryuki didn't exist then how Kamen Rider Ryuga would also exist? Well we just need to assume to here that the Mirror World didn't get reset and they still have the memory of EPISODE FINAL. Yeah, I know, TV Series and EPISODE FINAL are different stories which can't be connected. But remember, it's Toei. They can do anything. They are the true Oma Zi-O who can alter time & history (lol) without following their own rules.
Even when it comes to explaining why Kamen Rider Quiz even after Another Quiz was created, the Producer had come up with no proper explanation. Even when a fan asked a question regarding whether Kamen Rider Quiz is a Singularity Point, the Producer Shirakura had commented saying "He is just a Kamen Rider from the future".
Another Ryuki was born after Shinji transformed into Kamen Rider Ryuki in RIDER TIME: Kamen Rider Ryuki. How both Kamen Rider Ryuki & Another Ryuki co-exist at the same time? Well I can't explain that. Because it's Toei!.