This is a very long post. Without bias, I have done some analysis into how the possible consequences and repercussions this new type chart is going to affect the game. It is quite interesting to look at how each type is going to be affected by this change. some will change for the better, and others will change for the worst. I have done my own type evaluation and conclusion with how Fairy and these new type interactions are going to affect all the other types, and both the game and competitive metagame as a whole.
It is clear that with Fairy, many people are going to be required to carry a Poison or Steel Pokemon in their party. That is clear enough to say, as their type moves are not distributed as well as others. So! Here goes....
Types that have gained from from the new type chart
Ground We'll be seeing a lot more of them, especially as Poison and Steel are both super-effective against Fairy. Well be seeing more of Fire with a new resistance, so this is more good news for the type. Heatran will be running riot anyway so he needs to be in check. More Poison-, Fire-, and Steel-Pokemon? Earthquake will become even more prominent than it already is. Ground-types are going to have a field day!
Poison Obviously. Just watch out for those Earthquakes, and they'll be fine.
Ghost Should I use a Dark-type Pokemon, should I use a Ghost-type Pokemon, that is the question. Well, the answer is now you use a Ghost-type Pokemon because Dark has been shafted, receiving one weakness, and being resisted by another type, whereas Ghost has lost nothing. They're the same in the offensive department, so why would you pick a Pokemon with three weaknesses and three resists when you can pick a Pokemon with the same capabilities with only two weaknesses and two resists. And two immunities compared to the one for Dark!
Water Escaped the resistance from Ice this generation. Fire types probably will become further prominent anyway. Dragons won't be so rife so they'll be free to use their STABs at will. And as I said, Ground is gaining a huge boon here with this introduction of Fairy, so Water will come in use here.
Fire that resistance will sure come in handy.
Types that have lost from the new type chart
Fighting Its weakness to Fairy may be cancelled out by the likely commonness of Steel this generation, but we'll see. However, fighting is resisted by Poison.... Either way, I think that despite Fairy's introduction, Fighting is here to stay. With 5 strengths, it will always remain a force to be reckoned with.
Dragon HUGELY. I doubt it needs explaining.
Bug With almost every single type resisting Bug gaining significantly with this new type chart (that's Fairy, Poison, Steel, Fire, Ghost) and Dark falling into the shadows,Bug seriously has its work cut out to keep its head above the water this generation. That, and the number of types resisting it increasing to 7. Not good news for Bug.
Dark They seriously blew it here. Dark is now inferior, Ghost is now superior. See Ghost.
Ice Ice, oh Ice, what did you do to deserve such ill treatment by GF? Fairy has stolen your limelight! Ice's saving grace was that it was SE on Dragon, but why would use a Pokemon to slay Dragons that isn't even resistant to them when you can use one that is immune to Dragons!? And Steel- and Fire- types will be running riot everywhere thanks to Fairy, so poor Ice will be absolutely destroyed. It has gained absolutely nothing positive from this type chart. Looks like its further down in that huge chasm for you Ice, along with Dark, where it seems you belong according to GF. Well done GameFreak.
Grass Grass was hoping for a resistance against Fairy too, but that never materialised. Now it has to worry about these Poison- and Fire-types running around everywhere.
Steel is a mixed bag. It gains an effectiveness, but loses two resistances. This is especially bad news for Steel/Psychic and Steel/Ghost Pokemon. Steel has the advantage over Poison against Fairy as Steel has more resistances and Steel is immune to Poison anyway. However, Fire and Ground-types are going to start popping up everywhere. I don't know what to think about the Steel-type in this new type chart. It could gain, it could lose, we will see.
Lots of types have gained and lots of others have lost out. I admire their resolve in altering the chart, it was a big step, but in repairing some type interactions, they threw others into pandemonium. I think this new type chart is going to send us all into new chaos rather than into repairing the type chart. They could have played the Dark-Ghost relationship better and taken greater care with it. Earthquake will be spammed more than ever. And finally, by Gen VII, people will be mistaking Ice for a new type, before being reminded it actually existed in generations gone by.