Yes

The rooms at the Horseshoe is the same as they were when the hotel was called Bally's.
I was just there last month and did not see any difference. Of course the rooms at  Resort World are newer and better.
I will say I was not overly impressed by the Hilton rooms at the Resort World I though Conrad and Crockers was better.
Have fun in Vegas whichever hotel you choose

Park MGM is maybe a five minute walk, maybe a bit longer, through a hallway to the Aria poker room, closer than some of the hotel rooms in Aria.  The poker room at MGM Grand is not that far from the entrance on Las Vegas Blvd, so it's not that far via the pedestrian overpass from NYNY.  (And Excalibur isn't really that much farther.)  Depending on what events are going on, those can sometimes be as cheap or cheaper than Horseshoe.

Horseshoe Jubilee Tower is probably the shortest walk from hotel to poker room in any casino, if you have mobility issues.