How does ecology differ from biology?
Ecology has two meanings. The popular and the scientific meaning.

Ecology: the popular definition: Here the term ecology is probably quite poorly defined. To my gut feeling, the concept relates to the concept of global change. It encompass many fields such as biology (ecology (in the scientific sense), evolutionary biology and conservation biology especially), ethics and moral, politics, meteorology, public policy, ...

Ecology: the scientific definition: Ecology is a subfield of biology and earth sciences that studies interactions among organisms and their environment. interaction is an important word here.

Biology has a much broader meaning. Biology is the science that studies life. Biology studies the structure, the ecology (impact on their surrounding), the evolution, development biochemical processes, etc.. of living things. Biology is a very big field of science. A researcher in biology will probably not really consider him/herself as a biologist but rather as a molecular geneticist, a neurologist, a epidemiologist, a plant physiologist, a biochemist, a bioinformatician, a system biologist, etc.. For example, I would appreciate to consider myself as a population geneticist rather than as a biologist as there are many fields of biology I know nothing about. For example, I am a pretty bad naturalist.

In short, ecology is to biology what optics is to mechanics is to physics. Some people may not like this comparison as mechanics might take a larger part of physics that what ecology does to biology. Earth scientists may not like this comparison as well, as they are part of ecology without necessarily feeling like being part of biology. But anyway.

From the text you cite


  [..] as an ecologist [..] what gets me excited isn’t just finding out how the amazing plants and animals we find in the ocean work, but how they interact with each other and their environment [..]


It shows that indeed ecologist are interested in the interaction between organisms and between organisms and their abiotic environment. Matthew Fraser says "he's not only interested in how they work". 'How they work' is obviously an extremely inaccurate sentence. A less misleading reformulation would be: I am not interested in everything about the biology of marine animals, "I am especially interested in how animals interact with each other and how they interact with the environment", but obviously that is less exciting for the reader. The goal of Matthew I guess was to create the interest and the excitation of the reader (or audience) on ecology and for this purpose he kinda implied as ecology being more than biology, while ecology is only a subfield of biology.

For more information, wikipedia is your friend!