What is the origin and meaning of 焗烤
焗 as used in Cantonese means "to bake" in the most general sense of the word. The method of baking you quoted in your question appears to describe specifically to how the Hakka/Cantonese dish 鹽焗雞 ("salt-baked chicken") is prepared, rather than the meaning of 焗 in general, which is simply a method of cooking by surrounding heat. For instance, the word for "oven" in Cantonese is 焗爐. The word can also be used to describe baked cheese dishes for the simple reason that they are baked in an oven.

The character itself appears to be a relatively recent invention since it does not appear in dictionaries such as 《康熙字典》. It was invented by adding the 火 radical to the character 局, which shares the exact same pronunciation in Cantonese (guk6). As for the etymology of the word, I found several sources indicating that it historically should be written 焅, which does have an entry in 《康熙字典》 that cites definitions referring to dry or hot air:


  《說文》旱氣也。《廣韻》熱氣也。


In modern Cantonese usage, the word can be used similarly to refer to hot and stuffy air. The meaning "to bake" was probably a logical extension of this original meaning.

I found this post on a forum that quotes an entry in 《追本窮源：粵語詞彙趣談》 with more details:


  “焅”今通作“焗”，本義是“熱氣”，就是指酷熱的意思。“焅”解作烹調方法，在宋代的書籍已有記載。現在“焅”也解作烹調方法，有兩種含義：（１）利用蒸氣使密閉容器中的食物變熱。例如：“焅飯”；（２）密閉式的烘烤。例如：“焅番薯”、“鹽焅雞”、“芝士焅龍蝦”。其中“芝士焅龍蝦”是西菜。看來“焅”這種烹調法是宜中宜西的。
  
  由於“焅”的本義是“熱氣”，故引申為天氣悶熱，如說：“今日成攝氏三十八度，天氣好焅。”（“今天氣温接近攝氏三十八度，很悶熱。”）另外，空氣不流通，令人窒悶也可稱“焅”，如說：“間房冇開窗，焅死啦！”（“房間不開窗，悶死了！”）又“焅”有“強迫”、“被迫”的意思。例如：“佢唔鍾意食椰菜花，唔好焅佢食。（“他既然不喜歡吃椰菜花，就別強迫他吃了。”）“個股市係咁跌，焅住要斬倉。”（“股市指數不斷下滑，被迫要結算。”）“焅”在前句解作“強迫”，後句解作“被迫”。


For the benefit of the general audience, here's my own English translation of the entry:


  焅, now commonly written 焗, originally meant "hot air", referring to extreme heat. Its usage to describe a cooking method is attested by Song Dynasty records. 焅 as a cooking method now includes two meanings: (1) using steam in a sealed vessel to heat food, for example, "baked rice"; (2) sealed baking, for example, "baked sweet potato", "salt-baked chicken", "cheese-baked lobster". Of these, "cheese-baked lobster" is a Western dish. 焅 can be seen as appropriately describing both Chinese and Western cooking methods.
  
  From 焅's original meaning of hot air, its meaning is extended to hot and muggy weather, for instance: "Today will approach 38°C, the weather is very muggy (焅)." In addition, it can be used to describe the effect of air in a room that is stuffy and not well ventilated, for instance: "The room's windows haven't been opened; it's suffocating (焅死)!" Also, 焅 can mean "to compel" or "to be compelled", for instance: "He doesn't like cauliflower; don't compel (焅) him to eat it." "As the stock market continues to fall, I'll be forced (焅) to liquidate." 焅 in the former example was used to mean "compel", and in the latter used to mean "be compelled."