Seeing your save, I think I know what happened. Your Machoke learned Strength through level up and then you explored Mt. Coronet and did that place before Regirock's room. When I tried it, fighting Team Galactic in there first and then going to the villa to the right of the Pokémon Center for...
If you have strength and rock smash, you could travel all the way back to Snowpoint City from the Oreburgh Gate or the other side of Sinnoh if you have a bike and can go up Route 207 and the sailor in Snowpoint City will take you back to the Fight Area where you can then reach the Survival Area...