It is a step how to use coffee filter.
圧着部分を図１，２のように交互に折り込みドリッパーの内側にピッタリと装着します。
In my opinion, it should be
圧着部分を図１，２のように交互に折り込み - Fold the filter alternately following to the diagram 1 and 2 to be crimps.
ドリッパーの内側にピッタリと装着します - put the folded filter onto the coffee dripper firmly.
Otherwise, it should use て-form verb to combine the 2 activities like this: 圧着部分を図１，２のように交互に折り込んで...
Often, especially in formal/written Japanese it is customary to connect two sentences using the pre-masu form (let's call it this way to be consistent with the reference linked below), that is, the -masu form without the ”ます” (for example: 食べる → 食べ, 行く → 行き, and so on).
Think about this very common sentence for example: 。。。して頂{いただ}き誠{まこと}にありがとうございます。
I think your example is pretty much the same thing, and there is nothing wrong in connecting a chain of events/sentences in that way. Since it is probably an instruction manual the thing you are talking about, it makes sense that they use formal Japanese as well.
Some info and example on this topic: http://selftaughtjapanese.com/2014/05/14/connecting-ideas-in-japanese/
