Much more importantly, without UNIX and free beer TCP/IP there's a fair chance the Internet isn't the Network and none of this (gestures at HN and the Web) happens. That's a much bigger impact than C which is just a programming language, even if you count the influence of NUL-terminated strings, and all the semi-colon languages (including even Javascript and Rust, which are very different from C but preserve the enthusiasm for semi-colons) the Internet as Network makes more difference.
In particular it's possible X.25 could have won. JANET (the tertiary education network in the United Kingdom) was exclusively doing X.25 until 1991, when it tries an experiment offering IP. Unsurprisingly free beer TCP/IP offers a cornucopia of interesting new toys and sites are very enthusiastic about JIPS (the experimental IP service) so that by 1992 the IP service is no longer an experiment but the primary service, with X.25 maintained only until 1997.
You do get the Network anyway of course, that's what everything is leading up to after Shannon, but you probably get an X.25 flavoured Network instead of the Internet, or some other system coming from another direction, and broad deployment might have been delayed into the early 21st century rather than the 1990s depending on exactly how things work out. Stallman's GNU project doesn't happen, Tim's toy hypermedia system either doesn't exist or is a small inconsequential experiment largely unknown outside hypermedia fanatics, and Linus Torvalds probably doesn't make an operating system kernel for his 386 microcomputer. It's a very different environment, C is small potatoes by comparison.