If you completely lose control that isn't really NTS, that'd be full on NTR (Unless him having no control was itself part of the relationship dynamic) even NTS games that lean more heavily into the cuckold aspects almost never have an MC with no control. That doesn't mean Eric is fully in control of everything either, and I'm surprised you feel that way when so many complaints have been about the exact opposite. Personally I find both takes misguided, Eric is sometimes in full control and sometimes has limited to no control. It's contextual, depending on the situation, the characters involved etc...
But I am a little confused how you play through chapter 5 and 6 and feel Eric is "always in control" when both things at the club and photoshoot got crazy to a degree he didn't anticipate.
CG likes to play with elements of give and take in regards to control.
And in regards to Anya, you don't know for certain what will happen, content with Anya and Eric was also teased as far back as chapter 3 - go replay the beach sequence when Anya is literally about to take out her tits for Eric for example. But that doesn't mean nothing will ever happen with her and Rob (doesn't mean it WILL either, I'm just saying there's no gurantees), she's a slower burn than other characters though she only just had her first minor sexual scene with another person.