My understanding is that your floor will be much more stable going the opposite direction of joists, as then they will be supported each ~16 inches. I don't know if vinyl flooring provides any additional support; in my house we are putting in maple plank, over 3/4 inch plywood that sits on top of the joists, yet still we will change the direction at one room transition so we cross the joists.
I would examine the thickness and robustness of the subfloor, and ask myself if the vinyl flooring brings with it any strength/support. But I am no flooring expert, just another homeowner also trying to figure things out.
Good luck!

I don't see a wall running from your front door to the back patio door. The walls by your front door end at the kitchen door, seems like. The longest wall I see in your house runs east-west - the wall in the kitchen that contains the patio door (the door being part of the wall area). So that jives with the east-west direction to jive with the joist rule.

Are you placing your vinyl planks over an existing floor? What kind of floor?

The longest wall rule applies, I THINK, to a room. Not a whole house. The joist rule, which deals with stability, and creaks and such, would be more important than a long-wall rule.

But if you're putting vinyl plank over an existing floor, I'm not so sure the joist rule applies. Maybe. But I'm not sure about that.

I checked into this issue when considering vinyl planks for my bathroom. I looked at a lot of pics on the internet, read some flooring sites, etc. I found the joist rule, but since I was placing vinyl planks over ceramic in the bath, that didn't apply. I did find out that for planks in one room, there is no hard and fast rule as to whether they have to be in the direction of the longest wall, or the other direction. I also discovered there's no hard and fast rule as to whether one can go a different direction in one room from other rooms.

I can tell you how it is in my house with wood floors. All throughout the house, the wood planks go across the joists, per the joist rule, in every room. Even in the hall, which means the planks do NOT follow my 14 foot long wall, but rather go horizontally all the way down the hall. Visually, this gives a consistency and flow to the house. And there is a "stability" reason for the joist rule.

But I did discover that if I wanted to do my planks in that bath a different direction, that would be fine, if visually it looked okay (and preferably didn't abut right up against real wood planks going a different direction, which it wouldn't have).

For your house, though, your rooms seem mostly square, so that you don't really have any any wall expanses that are much longer than the other wall expanses in each room, except for the kitchen.

I will say that although my house is over 50 years old, the floors do not squeak much, if at all . So I think the joist rule is a good rule that exists for a reason. As I said, the longest-wall rule is a rule PER ROOM, is my understanding, and not one for the whole house. In reading about it, I discovered that a lot of people do not follow the longest-wall rule. If you're doing just one room, and you don't have to follow the direction of planks in the rest of the house, you can put planks in that one room in any direction you think would look best.

My personal preference, if you have planking throughout the whole house, is for all planks to run the same direction. Esp. if the house is small. It really has a consistency and flow to it, as you go from room to room.

I'm placing the planks over existing vinyl floor, which is already on top of a thin linoleum floor. The employee from the outlet said the joist rule didn't really apply to the vinyl floor. Wood floor would be another story.

I dry layed some of the floor and I feel that it looks better going north / south as the incoming sunlight flows with the grain (albeit fake grain) of the plank. Going east west seems to only highlight the seams with the incoming sun.

RPDHockey, How do you like the Coretec? I'm considering it and can't find much information.