Yes.
Whether they are worshipping them as if they are God is another question, but bowing before them is indeed worship. From Ray's worship study (May 2007):
Well actually it is, you know, it is a form of worship. When you pay homage, reverence or humility to anything whether it be an object or a monarch or a pagan god or whatever, it’s worship, okay. But there’s more to it then that.
Strong’s concordance, in the Greek, there are several words, but this is the most prevalent used; worship - to do reverence, to adore, like a dog licking his master’s hand. That the example he uses, like a dog licking your hand, that’s worship. Or you know, like a man bowing down or kissing the Pope’s ring, or whatever. These are signs of worship.
Now in the Hebrew it‘s a little different, but same general idea; worship - to prostrate (that means to get down), bow down, humble, obeisance. That’s the definition of the word.
As you pointed out, the word is sometimes translated as worship, and several versions (KJV, ASV, WEB) use worship in Revelation 3:9.
Here are some more passages:
Isaiah 45:11-14
11 Thus saith the Lord, the Holy One of Israel, and his Maker, Ask me of things to come concerning my sons, and concerning the work of my hands command ye me.
12 I have made the earth, and created man upon it: I, even my hands, have stretched out the heavens, and all their host have I commanded.
13 I have raised him up in righteousness, and I will direct all his ways: he shall build my city, and he shall let go my captives, not for price nor reward, saith the Lord of hosts.
14 Thus saith the Lord, The labour of Egypt, and merchandise of Ethiopia and of the Sabeans, men of stature, shall come over unto thee, and they shall be thine: they shall come after thee; in chains they shall come over, and they shall fall down unto thee, they shall make supplication unto thee, saying, Surely God is in thee; and there is none else, there is no God.
Isaiah 49
22 For thus says my Lord Yahweh, "Behold! I will lift My hand to the nations, and to the peoples will I raise My banner high. And they bring your sons in a bosom pouch, and your daughters on the shoulders shall be borne,
23 and kings become your foster fathers, and their chiefesses your wet nurses. Nostrils to the earth, shall they prostrate to you, and the soil at your feet shall they lick up. Then you shall know that I am Yahweh, and those expecting Me shall not be ashamed.
Isaiah 60:14 And go to you to prostrate shall all the sons of your humiliators, and worship at the soles of your feet shall all your spurners. And they call you the city of Yahweh, Zion of the Holy One of Israel.