Your G2020 dual core has a passmark rating of 2783 and a single thread rating of 1544.
A I3-3220 will be 4209/1761.
Such an upgrade should be inexpensive and reasonably effective if you can buy used.
A I3-6100 has a rating of 5500/2102.
If your games are sims, mmo, or strategy games, I would go with the stronger chip.