It would seem unlikely, but certainly not impossible, to have a TV that new without an HDMI port. But if it truly does not have an HDMI port, then no, your Roku is not compatible. The Express+ is the only Roku with analog outputs, but that of course doesn't support HD audio.
I would look over the TV more closely for an HDMI port, or at least the model number so we can verify its capabilities.
Dan
Roku Stick (3600), Ultra (4640), Ultra (4670), Ultra (4800), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Nvidia Shield, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.