No, it does not imply that other gods exist. It implies that we might attempt to worship what we think are other gods.
In the ancient world the concept that there was but one God was a unique and strange idea. The Jewish people were probably the first to proclaim the idea. The Jewish people were, however, a relatively small group of tribes. In their interactions with virtually every person and nation they encountered the issue of other gods in the religions of others would have been present. At various times in the history of Israel they were conquered by polytheistic groups that demanded worship of their gods. Sometimes such worship was coerced with the threat of death and produced Jewish martyrs. Other times and for most people, the issue would have been social exclusion from the rest of society. It would have been easier to “go along to get along” in order to reap social or personal benefits.
The commandment was understood by the Jews as saying that there are no other gods and do not fall into the trap of honoring other false gods. The commandments were considered instruction on the right worship of God, essentially declaring that people can’t have their cake and eat it to. You can’t declare God to be the sole God and then give honor to false gods on the side.
There is nothing in Jewish tradition to suggest an inference to the actual existence of other gods. We cannot impose a context that was not present.
