Yes, big time, even a quad core version of your CPU would be a bottleneck. Most new games require at least 4 threads to function properly, with dual core CPUs that lack some sort of multithreading capability having issues even launching the game, or suffering serious performance issues like stuttering and very low framerates, and that's with much better dual cores than what you have like the Pentium G3258.
You need to look at doing a complete rebuild of your system to run the latest games, a simple GPU upgrade isn't going to cut it.