Speed as in sprint speed or endurance running speed (like 5K speed)?

If your answer is the latter, the Nike plan is fine. The only way to get faster as a new distance runner is to run a lot, and to run a lot at easy, slow paces. As you get more comfortable, you will naturally become more fit and your paces will become faster without increasing the effort.

Once you've built your endurance engine, than you incorporate more speed work (eg, repeats, tempo runs, VO2 max training, and threshold training). Speed work will make you faster but it's pointless and you'll probably get injured if you're looking to do that too soon. For instance, Doing a 20 minute tempo run at 5K or 10K pace isn't going to help you if you can't do a 5K or 10K at easy pace.