Has this exclusivity for the -115 prevented Airbus from developing a direct competitor to the 777 due to the lack of an engine available to power it.
You quote SMT Member's post without appearing to understand it.
The point that both SMT and I are trying (and clearly failing) to get across is that the exclusivity is in the opposite direction to that which you are implying.
To put it simply:
Boeing agreed with GE that the GE90 will be the only engine offered on the 777-200LR/F/-300ER - TRUE
GE agreed with Boeing that GE won't offer the GE90 to any other manufacturer (e.g. Airbus) - FALSE
It follows that there is no constraint preventing Airbus building a 777-sized, GE90-powered aircraft should they wish to.
The fact that they haven't is doubtless because they don't think the market is big enough, and they have their hands full with the A380 and A350, not because GE won't sell them an engine.
Please let me know when I can stop banging my head, it's starting to hurt.