arc is used to transmit audio from a normally hdmi input only (such as on a tv) to a device which supports this on a normally hdmi output. generally this means tv (input) to receiver/htib (output) with both supporting arc. otherwise, it does not have much function.
it looks like your projector takes hdmi in and has 3.5mm out for audio. it looks like your soundbar has hdmi in, hdmi out and 3.5mm in for audio.
this leaves you two apparent connection options:
pc->soundbar via hdmi and soundbar->projector via hdmi. assuming the in/out is passthrough on the soundbar of course.
or... pc->projector via hdmi and projector->soundbar via 3.5mm.
given that its a soundbar with 2.1 capability only it really does not matter how you connect...