I agree with most of the comments here. C/C++ are great to learn to use but they are fazing out in a lot of more common areas. They still have their place and will probably have their place for a very long time yet to come. Learning will make you a better programmer overall even in more modern languages. For games you really do not need C++ or C. There are lots of great technologies out there today that are beyond capable of keeping up. Heck even today much of the games you play are done with scripting languages and those languages hook into the C++ rendering engine on the backend.
The main reason I say C/C++ will be for around for a long time is mainly because of specific areas like kernel development as well as embedded micro controller development. Sure there are new languages coming out that are compiled to machine code like Google's Go. The big downfall of those types of languages is the lack of direct memory access through pointers and direct interfacing with assembly code. In the world of Kernels and embedded micro controller (think ARM Cortex M, PIC, AVR) you really need that otherwise you can't really do anything without extreme C interfacing hoops. Some of those chips are so tiny in memory you would be lucky to get a runtime driven language on them. These are extreme cases.
So in the end if you are learning your first language I would recommend it not be C++. I would rather see a new programmer on their first language use pure C, C#, Java, or Python. C is a very simple language to learn and will let you learn some really useful concepts this is still my all time favorite language. C#, Java, and Python are also relatively simple languages that rule out memory management and will allow you to focus on core algorithm concepts. Choose something you want to choose not what everyone forces you to choose and stick with it for a while before moving on. Every language you learn will teach you something new.