As I have indicated previously some of the Hebrew words used in Shmot/Exodus 20:3 have more than 1 possible meaning. Depending on which meaning you choose you could get a somewhat different message of what the verse is telling us.
The following is the Gaon Rabbi Achai view in Sha'eltot in Hebrew of the prohibition listed in the verse followed by my translation of his words
שאילתות דרב אחאי פרשת יתרו שאילתא נב
דאסר להון לדבי' ישר' למפלח לשום מדעם בעלמא ולאודויי אלא להקב"ה לחודיה שנאמר לא יהיה לך אלהים אחרים על פני וכתיב לא תשתחוה להם ולא תעבדם
That it is forbidden for the House of Israel to worship to anything in this world and/or to admit (alt. translation, to offer thanks) to it, except if it is to the Holy One Bless Be He, alone, for it was stated...
After the word "for it was stated" he quotes our verse of Shmot/Exodus 20:3 and then adds a quote of the first part of Shmot/Exodus 20:5.
My understanding of why he added the additional quotation of the first part of Shmot/Exodus 20:5, is to show the context of the paragraph which he understood as supporting his interpretation.