Stained last summer, want to redo

Last year we did our angelum pedra deck with SuperDeck's Exotic Hardwood Stain. The deck is on the SE corner of the house and uncovered so it gets a lot of sun. We moved our patio chairs (large, living room style chairs) and it shows that the deck faded quite a bit in one year. We'd like to give it another coat as I'd like to get to it before it's too worn. It's not greyed, it's not flaking, just faded.

Do I need to use a cleaner and brightener before redoing? or can I just clean with TSP or something along those lines? I did take a look at the cleaner and brightener last year and they were definitely more time consuming and needed more care than a simple soap cleaning. LOL We've got very few days left with acceptable temps for staining so I need to balance doing things perfectly with doing it acceptable. For example, I'm not hugely bothered if the area with the chairs stays darker, as the sun chairs are going back in the same spot next summer and the sun still has time to play catch up as it's too cold already to sit outside so the chairs are put away.

I know this has been left late, but I promise we weren't just lazy. We had to do the entire landscaping of our backyard and put up and stain a fence so our kids had a yard to use this summer. There never seems to be enough time.

I guess the other issue is that we need to do the cleaning tomorrow and there is nowhere that will be open on Sunday (or the Monday holiday when we need to stain) to purchase the SuperDeck cleaner and brightener. Home Depot, Rona and Canadian Tire will be open, but I don't know if their offerings are acceptable?

Editing to add pictures:

Faded deck:

Where chair was next to faded area:

Overall:

Note that the deck isn't clean yet, and the dirt gathered under the chairs so there are dirty patches too making it look worse.