1. Complexity of implementation is not complexity of use. Example: Take std::array vs a plain C array. std::array is a few hundreds of lines of code. But - it's about as inutitive to use; has more convenience features; easier for the compiler to optimize; and doesn't let you should yourself in the foot that easily.
2. If Whiting don't want _any_ of the features of C++ - his software-writing skills are suspect. Now, few people need or want all of C++'s features - but C's are definitely insufficient, especially if you consider both the langauge and some of the standard library (or non-standard common libraries).
3. The complexity you have to tackle with C++ is lower than the complexity of non-standardized often-inconsistent idiosyncratic platforms and libraries for achieving the same things with C (or C + assembly).
So I find Whiting's argument for C over C++ unconvincing. IMHO C++ would be the least-bad language for writing demanding games in.