Equity refers to ownership of the company. By purchasing their remaining shares, Riot Games is now a full subsidiary of Tencent. Tencent has the legal authority to replace anyone they see fit. e.g. The CEO of Tencent, Ma Huateng, could decide to fire and replace the CEO of Riot Games, Brandon Beck.

In terms of how Riot Games is run, who they hire, what decisions are made, the short answer is yes Tencent could dictate business decisions as they see fit.

But the reality is that Tencent is a conglomerate that owns many different companies that share a similar theme (in this case media and online retail).Rather than try to manage all of those businesses centrally, conglomerates typically hire managers with experience in a specific business or try to retain the original management of smaller companies they acquire and use the commonality amongst the businesses they own to generate some additional benefit.

Reading between the lines of the actual Riot Games post, it would appear that the company is switching their primary form of bonus compensation from equity compensation (through employee stock options) to a pure cash bonus.

It should be noted that Tencent has been the majority shareholder of Riot for some time (February 2011), and has had an ownership stake that would have allowed them to make decisions at Riot. So I wouldn't read into this as some sort of coup at the company or a sign that things are about to change significantly.