It doesn't have to be a overall old build, it could just have older gameplay. The teams can work in parallel.
I won't go too in-depth on version control systems (like Git), but there can be many branches of Madden being worked on in parallel, this is to keep the teams from getting in each others way. The gameplay team can have their own branch that only they change and the same for the presentation team, the MUT team etc.
They are then worked on in parallel and the teams changes are occasionally merged together so they get the updates from the other teams, but then they all continue working on their own branches.
For the last stream the gameplay team showed their latest fairly stable build. Then for this stream the presentation team showed
their latest fairly stable build. Now in between the two streams the two teams may not have merged their changes (Or not all of the changes. The teams could have many, many branches just for themselves and not merge them all at once.) and the last time the presentation team was working with the newest gameplay changes could have been months ago.
Of course this is all speculative, but EA has to be using a version control system of some sort and they all generally let you do things like this.