As answered by Efra, the reference is to the Chaldeans/Babylon and thus by inference to the king of Babylon of that time namely Nebuchadnezzar.
I would like to show how this can be determined by the literary context.
Hab 2:5 is a continuation of God's response begun in v. 2 to Habakkuk's question in 1:17:
Will they therefore empty their net And continually slay nations without sparing? (NASB)
Habakkuk's question concludes his second lament to the LORD in vv. 12–16:
Are You not from everlasting, O LORD, my God, my Holy One? We will not die. You, O LORD, have appointed them to judge; And You, O Rock, have established them to correct. 13 Your eyes are too pure to approve evil, And You can not look on wickedness with favor. Why do You look with favor On those who deal treacherously (בּוֹגְדִים)? Why are You silent when the wicked swallow up (בְּבַלַּע) Those more righteous than they? 14 Why have You made men (אָדָם) like the fish of the sea, Like creeping things without a ruler over them? 15 The Chaldeans (lit. he) bring all of them up with a hook, Drag them away with their net, And gather them (וְיַאַסְפֵהוּ) together in their fishing net. Therefore they rejoice and are glad. 16 Therefore they offer a sacrifice to their net And burn incense to their fishing net; Because through these things their catch is large, And their food is plentiful. (NASB)
Notice that the wicked here are described as "those who deal treacherously (בּוֹגְדִים, bogdim)" and who "swallow up" those more righteous than them and "gather" these men——adam, humankind——like fish in a net. In Hab 2:5 wine "betrays (בּוֹגֵד, boged, same verb)" the haughty man and this haughty man "enlarges his appetite (נֶפֶשׁ, nefesh)" and "gathers (וַיֶּאֱסֹף, same verb) to himself all nations (הַגּוֹיִם)". The base meaning of nefesh is "throat". This is probably the meaning here. Nevertheless, whether one understands nefesh here to physically mean "throat" or figuratively to "appetite" there is a literary connection between the description of the treacherous swallowing humankind like fish gathered in a net and the haughty man who betrayed by wine enlarges his nefesh to gather nations.
The NASB rightly identifies the "he" of v. 15——and thus the wicked and the treacherous of v. 13——as the Chaldeans. This identity has just been revealed in vv. 5–11 in the LORD's response to Habakkuk's first lament.
"Look among the nations! Observe! Be astonished! Wonder! Because I am doing something in your days - You would not believe if you were told. 6 "For behold, I am raising up the Chaldeans (הַכַּשְׂדִּים), That fierce and impetuous people Who march throughout the earth To seize dwelling places which are not theirs. 7 "They are dreaded and feared; Their justice and authority originate with themselves. 8 "Their horses are swifter than leopards And keener than wolves in the evening. Their horsemen come galloping, Their horsemen come from afar; They fly like an eagle swooping down to devour. 9 "All of them come for violence. Their horde of faces moves forward. They collect captives like sand. 10 "They mock at kings And rulers are a laughing matter to them. They laugh at every fortress And heap up rubble to capture it. 11 "Then they will sweep through like the wind and pass on. But they will be held guilty", They whose strength is their god." (NASB)
The Chaldeans is another name for the Babylonians.