The HDMI port on your MacBook is an output, not an input, so that won't work. But I don't think there's anything available on Roku that's not also available via the web, so you should be able to get all the same content.
Thunderbolt is, depending on your Mac, either one or two 10 Gbps bi-directional streams in the case of Thunderbolt 1. Thunderbolt 2 ups that to 20 Gbps. The MacBook Air is too thin for a full-sized controller, so it gets a single bi-directional stream, other Macs have dual bi-directional streams. The Thunderbolt port is compatible with MiniDisplayPort displays. Otherwise Thunderbolt can provide audio, video, data & power to external devices like Apple's Thunderbolt display or various brands of hubs. What I'm trying to say is that Thunderbolt is not a one-way connection but the visually-similar Mini DisplayPort is output-only.
I once connected a Thunderbolt hub to a MacBook Air & was able to connect four external HDs, one via Thunderbolt, one via Firewire 800, one via USB 3 & another via USB 2. This left a USB 3 port unused, so I connected a DVI display via a Display-Link USB adaptor. Everything worked fine, indicating two-way compatibility with HDs & one way with a display. I suspect you have a HDMI - Mini DisplayPort cable, rather than HDMI - Thunderbolt. Answered by Peter E from Pakenham. Jun 26, 2015.
Matrox MXO2 Mini Currently the only solution for laptops I'm aware of (as I have been doing allot of research for this option on a MacBook Pro for pro video use) Is the Matrox MXO2 Mini LAPTOP version (US$449). You need a ExpressCard /34 slot (there is also a PCIe version) I have not used this device myself, however I have used the more expensive competitor, the AJA IO Express which is about US$900. And this does still have a very slight lag even on the top of the line MacBook Pro laptops which would make live gameplay difficult. Note, that these devices are designed for Pro Video applications.
Saying all that, I do know that there are computers such as the new iMacs with displayports that allow video INPUT using a cheap adaptor (DVI, HDMI input) and this may become an option with the newer macbooks soon i'm guessing, in this case, its an interface directly to the display, and not a video i/o device that works thru the computer itself, it would not have a lag associated with the input. Click to expand.' No, no and no' is not exactly correct, but I appreciate the response. Yes, my receiver converts and outputs HDMI but No, I cannot input into the minidisplay port, you're right. And Yes, HDCP would be a problem.
True, I agree that an analog to usb converter would work, but it could also be output through firewire and inpiut into the MBP that way as well. For HDMI I would need something that would convert to one of those two types of connection (usb or firewire), as long as it also deals with the HDCP issue.