It first matters what country is involved, because the specifics of copyright law differ in terms of how research use is treated. Copying for research purposes is generally treated favorably, but there is no blanket "if it's research it's okay" exception. In the US, you would be relying on the concept of "fair use", a defense where the court decides if things balance out in your favor. The problem is that fair use operates in terms of "balancing" plus a tie-breaker "transformativeness" criterion, and it is difficult to compute the outcome in advance. Therefore, you would need to hire an attorney that specializes in copyright law, to do an analysis of your legal risk based on all of the details of your plan.
Let us suppose that you are writing a doctoral dissertation in an area of arts and humanities on an artsy aspect of music in Doom 2. You collect AV data playing the game, then perform some kind of analysis, where you might e.g transcribe a handful of samples and include a few screen shots of the video. You do not post the raw data anywhere. This is most likely to pass the fair use test. Your copying is highly transformative (turns compute code into musical transcriptions and prose description of the tunes). Your dissertation has no (negative) effect on the market for the product, and it is for a non-profit educational purpose. Since you are copying the automatic output of a computer program, it is not clear how much is actually protected, but we can say that the drawing of the pink things is protected, but the specific configuration of pink and green things is not, that is a non-creative automatic calculation. To assess the "substantiality" of the copying, you would have to engage in a nuanced analysis of what things in the game are human-created, and what things are algorithmic responses.
There is a separate question you might want to consider regarding contractual commitments, depending on whether you are doing this as independent research, as an employee of some business, or a student or staff member at an educational institution. E.g. they may require you to obtain permission, and refuse to accept your work if you don't comply. But make that a separate question.
