Yeah, the moviemate series from Epson has a built in DVD player and some relatively decent internal speakers for a projector. Nice for instant movie night. No Blu-ray built in, but it does have HDMI on that model. Other models didn't have the HDMI input. I didn't even know they still made these models, I'm not sure if this one is even in production.
That said, my main concern would be that the digital audio output may not be for all sources connected to it. It may just be for the internal DVD player to feed an A/V receiver.
I would definitely go the course of an A/V receiver. Depending on what is to be watched, there are any number of newer models, but an older model of higher quality and power may be a good deal for this specific setup. That is, more power for the speakers and no need for the latest HDMI specification since the projector doesn't support anything higher than 720p resolution natively.
Still, I'm not sure that just using an external source with analog audio out, or a HDMI audio extractor and a good powered amplifier may not be a better overall deal.
ie:
https://www.ebay.com/itm/Crown-XLS-402-450W-2-Channel-Power-Amplifier/202455645485?hash=item2f234bfd2d:g:KkoAAOSwme1bsoWJ
That's under $100 and will provide plenty of power. Then you just need a source to feed the amplifier separately from the projector. You can extract audio directly from HDMI using something like this:
https://www.amazon.com/J-Tech-Digital-Premium-Extractor-Converter/dp/B00BIQER0E/ref=sr_1_3?s=electronics&ie=UTF8&qid=1538515156&sr=1-3&keywords=hdmi+audio+extractor
Then a couple of RCA to XLR cables to connect it from the extractor to the amp...
https://www.amazon.com/Stagg-STC3CMXM-Male-Twin-Cable/dp/B003SOR6UC/ref=sr_1_6?s=electronics&ie=UTF8&qid=1538515209&sr=1-6&keywords=rca+to+xlr+cable
So, for about $150 you get more power to those speakers than almost any receiver is likely going to give you. You lose the simple switching, but you get HDMI connectivity for the setup.