I'll do my best. There's a lot of specialized terminology and I can't help you much with "proposing some theoretical adjustments to the multilevel game theory", it may be perfectly correct.
The main change is a matter of singular or plural. I believe it should be "framework of this approach" because the approach you are referring to is the "tendency to place at the centre etc"... hence, singular.
I would leave the apostrophe out of 90's (e.g. 90s) but many people don't. '90s is also common.
Relations between Russia and China have evolved significantly since the adoption of the border agreement in 1991. However, studies examining these developments traditionally tend to place at the center of their analysis, the opposition between the federal executive and the peripheral regions over Russian policy in Asia. The analytical framework of this approach thus ignores the unique role of local communities. We propose here to examine the influence and the role of these local communities throughout the evolution of Sino-Russian border relations in the 90’s. In order to do this, we will reframe our analysis of the interactions between the authorities and local mobilizations, by proposing some theoretical adjustments to the multilevel game theory. We will then review the role of the local communities in two of Habarovsk’s regional issues – cross-border trade and territorial concessions.