We just don't hear his thoughts. Also, Nagato was the one who got the least amount of snarky thoughts at anyways.
This is a split off timeline from Disappearance of Haruhi.
The alternative Yuki is just too much like normal Yuki if you dumped her personality into a normal human body (with hormones/emotions) and Do!Yuki's memories to go by. The head injury temporarily reawakened the original Nagato, partially. Basically Disappearance of Haruhi was Nagato rewriting reality some, but holding back for concerns of what Kyon wanted. When Kyon in this timeline accepted the changes the rewrite became more drastic. This would help explain differences between Haruhi, Do!Haruhi, and Do!Yuki.
- Do!Haruhi's Haruhi being more subdued and normal until Kyon breaks through to her compared to Do!Yuki. In Do!Haruhi Yuki was probably exerting extra effort to keep Haruhi out of the picture. In Do!Yuki there is no need so Haruhi is back to her normal self. Note that Do!Haruhi also happens to be out of the picture exactly for how long Alt!Yuki is around and not a moment sooner or a day later. Alt!Yuki was probably tapping into the "god" powers subconsciously to remove Haruhi from the picture as she did with Do!Haruhi, but couldn't be as drastic.
- Asakura's reaction and being the first to notice Alt!Nagato not being Nagato. Not "what's wrong", but accusing her of being a different person entirely. Either an extreme low level reverting to her role as Nagato's "safety" as seen in Do!Haruhi (no need to self-realize her role or go knife nut, yet) or a vestigial piece of it that wasn't fully removed.
- Some things seem inevitable. The Remote Island Mystery seemed to happen despite the SOS Brigade not being there. Kyon still helped Haruhi send her message, but this time it was a three year-younger Kyon. This implies when Do!Yuki's full rewrite happened it was still limited in what it could do. So some things took priority. She could remove time travelers bringing Kyon to the past, but not him helping Haruhi. So middle school Kyon got shunted there instead.
- This also hints that the prime!Haruhi timeline may not even be the original. Maybe originally a middle school Kyon helped a middle school Haruhi. Only the Time Travelers began tweaking the events (bringing a high school Kyon to fill the role) to fit their schemes.