The word used in the original Greek is pros-kyn-isan-tes ("[they] having fallen down and adored") and means to fall down in order to venerate someone (or a visible demonstration of veneration toward someone), and it is not necessarily (although many times) used in reference to worship of God. The English word "worship" comes from Old English weorþsċipe (...
There was some controversy over the phrase in the 80's because some minority of manuscripts appeared to omit the phrase which led to some Bible versions removing it or footnoting it. However, earlier manuscripts were found in the 50's that did have the phrase in it which make the later omissions likely scribal errors (mistakes). It has since been restored ...
I am not an expert at all on hermeneutics but I hope this can help. The original word used is "proskyneō". The literal translation is "to kiss" or to lick as a dog does to his master. The same word is used frequently in the Gospel of Matthew. The Latin word used in the Vulgate is "adorantes", which also can mean "to worship" or "admire"
Luke 24:52 NASB
"And they, after worshipping Him, returned to Jerusalem with great joy"
Yes, the Greek word "προσκυνήσαντες" is talking about worship.
Here's the Greek word used: