There is no such word времяёмкий in Russian standard dictionaries yet.
The article that Olga found is about experimenting with language. People suggest some words. These words are not in dictionaries yet and perhaps will never be.
I agree with comment by hazzic to the OP (Aug 10) that Google Translate is not a reputable source to conclude if word exists or not. It can return translations that are very far from perfect.
Dictionary of Zalizniak (1980) gives only 7 words ending with -ёмкий. (I ordered them by the frequency, defined here as the number of web-pages found by yandex.ru with the word:
трудоёмкий 5 mln
энергоёмкий 1 mln
Not in Zalizniak (1980) but on internet:
Among the pages found with времяемкий: on top was the page quoted by Olga which is kind of experimental; many pages were using this word enclosed into apostrophes to show that the word was invented on the spot for brevity, and many could just be attributed to an erroneous usage.
In 10 years from now this word may become a first class citizen in Russian, but now it is on the brink of existence.
Maybe in 10 years I will use this word, too, but now I wouldn't because ёмкий has positive connotation in Russian. For spending time I would prefer to use времязатратный.