I may be wrong, but it looks like a literal attempt to replace you. She is deliberately defying you.
You should tell her straightout: That is MY seat, do NOT sit there EVER again! DO YOU UNDERSTAND?

In general but especially with my boys (BS13 and SS18) I will talk twice - if needed.  I often think I get my point across the first time, so once is often enough.  As someone may not have understood the first time despite what I observed, I will make the same point a second time - and check if you understand by asking for a rephrase of what  I mean.  Then I KNOW you have got the message.
There is no THIRD TIME because by then I assume your attitude to what I said is "eff that noise".Then there are consequences... And Myss Nice Tique is no longer in the building. (I very rarely  get to this stage with the boys or anyone else.)

It's not about the "small" things - because they seem small we tend to let them slide sometimes. But add up everything and it is combination of small seemingly stupid stuff that make you explode! Also the "small" stuff is often an indicator of a larger problem or overall attitude... It still needs to be addressed IMO.

Hahaha yeah. I had a similar situation involving a chair. I got a rocking recliner from my grandma for when my YDS was born and SD decided it was hers so she would put all her blankets and stuffed animals on it to claim it. And then I would move them all to sit in it and she would sit there and glare me down. Eventually I asked why she was glaring at me and she quickly said she wasnt. Idk how well it would work to just directly confront her in your situation since my SD was quite a bit younger and still afraid to talk back to adults directly much. 

Passive aggressive would have been nice.
My  EX-SD was actively aggressive and violent!
Juvie time for violence.

If she sits on your chair again, shove her off it.
Words don't work with her.
 

Ugh, the musical chair thing. I have the same problem here with my step daughter. When I can’t just let it roll off my back, I practice mini disconnect sessions from the step kids and Dad and just focus on my babies, chores, or whatever to keep me busy  

Whatever you do, don’t let it show that it bothers you in any way! I’m sure she is very observant of how it affects you when she does it, because it sounds purposeful   

Both of my step children can be passive aggressive. At 9 and 11, they are also experimenting with lying, testing what my role actually is in their lives, and doing things they know are wrong. 

I don’t have any advice for you since I don’t have experience with a 16 year old- I know the teen years are a whole other breed of discipline problems! I was a middle and high school teacher though, so I guess my advice would definitely be to stay consistent, don’t show your emotion if it’s negative or gives the SD an advantage over you (you don’t want her to think she has power or control), and don’t let the situation as a whole bring you down- at 16 I’m assuming she won’t be a huge problem for very long. 

Have you experimented putting your cup in other seats and seeing if the same thing happens?

How supportive is your husband if you did say something to address it? 

Or you could be passive aggressive too! Say something like, “Oh hey, SDs name, I’m guessing you have been telling me you really want to sit with me since you’re always sitting wherever I put my cup!” And just kind of sit down in the same seat with her with a smile on your face.