If we go by paper date it was 110 years ago ...

The title in english is "On the Electrodynamics of Moving Bodies" ...

the important thing here is, that they showed through maths (based on todays understandings) that their proposed setup has a good chance of detecting photon-photon reactions

there isn't enough money and resources to just build every setup people come up with, so it's very important to be able to proof mathematically, that in theory this should work

and if it doesn't that's an exciting result aswell, as it could indicate our models can be further tweaked or unknown effects/interactions still linger out there waiting to be found

In the broad sense, yes, the theory is 110 years old, but this specific possibility which yes, uses that theory as a basis, wasn't hypothesized until 1934z

What theory exactly in 1934 ? 

Cause general relativity which uses special relativity as a basis was thought up of only 10 years after special relativity which is about 100 years ago ...

No theory in 1934. In 1934 it was hypothesized that 2 photons could collide and form a positron and an electron, which is what these scientists have figured out how to test.

Oh so they proved a conjecture of a consequence from special relativity ... 

Not sure how this changes anything as we already had proofs for special relativity itself for quite a while ...

No one said it changes something and has massive implications, however proving concepts can never hurt.

I think we've wandered far off from the beaten splintered path ...  

But what was actually a 1934 conjecture was just a 1905 theory ...