Yeah, the absence of a preposition is weird - I get tired of or by things or activities, at least in English.
The absence of a preposition makes me think that a valid translation might be "He gets tired working" - the English gerund is often replaced by the infinitive in non-English languages.
I think that "He was tired by work" might be OK, but I'm guessing. Other comments elsewhere suggest that he is tired now because of the work he did before, which more-or-less mixes English past and present tenses.
Also, устал is perfective aspect, which I believe indicates that something is completed - the work, that is, tiring him out, so that contributes to the is tired now from what he did before.
I have a pronunciation question. The audio pronounces работать with a kind of "-titch" sound for -ть at the end of работать. Most (but not all) of the 11 recordings do the same thing at https://forvo.com/word/%D1%80%D0%B0%D0%B1%D0%BE%D1%82%D0%B0%D1%82%D1%8C/#ru
Some of the recordings state a clearly defined "tat" ending sound.
I've heard the "-titch" sound in the pronunciation of other infinitives.
I had this explained to me in another exercise yesterday. The -ть sound is more like a ч than the English titch sound so that it defines it from the hard т ending when the word spelling is identical, apart from the soft sign, eg he/she cooks-готовит, to cook-готовить. Personally, in rapid speech, I have no chance of picking it out!
He is tired of work. He lost interest in working (work). He became bored with work.
Adjective: I am tired. I had a lot of work today. I rubbed my tired eyes.
Verb: to tire is to feel in need of rest or sleep The long journey tired her. The training tired us out.
This is how I understood it.