Congress creates laws. The President enforces them. This is an enforcement action--it's not unusual for Congress to be uninvolved.
> Should the president really have this power?
Multiple Congresses gave these powers to the President [1][2][3]. The current and next ones are free to take them back.
My personal belief is no, the President shouldn't have this power in the absence of clear and present danger. We need a commission, likely under Commerce and/or State, that assesses civil fines and passes prosecution recommendations to the DoJ. Furthermore, we need legislation describing (a) which countries are deemed economically friendly and economically adversarial, (b) how those determinations are made and (c) what companies from those countries can and cannot do as well as (d) how they may achieve "safe harbor" status (e.g. by locally hosting data and submitting code for periodic review).
[1] https://en.wikipedia.org/wiki/International_Emergency_Econom...
[2] https://en.wikipedia.org/wiki/Exon–Florio_Amendment
[3] https://www.treasury.gov/resource-center/international/Docum...