Rather than thinking about maximum length, focus on maximising engagement and readability by using appropriate headings, typography (line length, font size, line height, etc.), and producing high-quality content.
Headings for each series/game will likely vary. For example, if the series is heavily dependent on geography (think: Game of Thrones), you'd likely want a section highlighting plot points in each area. However, there are two headings that will likely exist for all games/series: Summary and Characters.
- An overview of the entire game / season
- the major plot points
- A list of the characters, and their major plot points in the season
As Shreyas suggested, I'd strongly recommend breaking the summary into chunks. However, chunking is just the first step. To ensure readability, you have to pay close attention to your typography.
You have to make it easy to read. Here's a great article on how people read, including recommendations for measure, font size, and line height. To summarize:
Measure (a.k.a. line length)
- Aim for between 45 and 85 characters per line
- 65 seems to work very well
- Both too big and too small create problems
- Size of font will depend on the viewing device
- On a desktop, use at least 16 px for body copy
- The horizontal space between your lines
- No perfect line height, but 150% of your font size is a good guideline
In addition to the text descriptions, depending on the available resources, you might consider adding additional content.
Having video recaps of each game or season might be helpful. Some people prefer to watch videos than to read. With a transcription, users can search the video to search for specific information.
Another thing to consider is adding a high level visual timeline of the series / show. This would require some graphic skill, but would provide a high level overview of the major plot points in the series at a glance. I'm envisioning a chart, with the x axis as time (start to finish). Each season could have a slightly different coloured background, and the major plot points (for each character, region, or whatever is appropriate for the game/series) are plotted along the Y axis. You'd have to think through this in more detail, but it would provide a quick synopsis of the plot without requiring a bunch of reading.
I think the most difficult part of your work will be to condense the material to provide a summary, but hopefully some of these ideas are helpful.