To my ear, the speaker sound like робЕти Is that simply the way it is in Ukrainian, or am I hearing incorrectly? Is every stressed и pronounced /e/ ?
Indeed, Ukrainian /ɪ/ is somewhat in-between [ɪ] and [e]. Wikipedia says that it can be transcribed as [e̠], [ë], [ɪ̞] or [ɘ̟] in precise transcription.
The Ukrainian vowel и is pronounced like the letter i in English words such as hit, kiss, sin, tin, list, etc.