Two things - first, it looks like the SCART on the Philips is an output
Second, doesnt the xbox1 only have one HDMI port? How will you get the picture through the hdmi to dvi and the sound into the amp?
You can buy HDMI audio extractors like these
https://www.amazon.co.uk/hdmi-audio-extractor/s?k=hdmi+audio+extractor
That would let you connect the xbox audio to the red and white inputs on the amp.
But, you're probably better going for something like this
https://www.amazon.co.uk/Converter-Control-Aluminum-Digital-Toslink/dp/B09WMDF6CH/ref=asc_df_B09WMDF6CH/?tag=googshopuk-21&linkCode=df0&hvadid=570317715727&hvpos=&hvnetw=g&hvrand=12173707414783470431&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=1007320&hvtargid=pla-1719137565807&psc=1
That way you can use the HDMI to dvi for the video and use the SPDIF audio output on the xbox and convert it to red and white RCA for the amp