Using the TV speakers for L/C/R is not the objective. The objective is to use the receiver's out (with whatever source) and output the analog L+R to a TV input. HDMI will be used for video and analog audio can be input to the TV. I have done this, but for a different reason. My TV is ALWAYS just a monitor. Whatever the reason, to have basic surround, this should be possible in this situation.
For now, it seems a waste of the potential of full surround, but with 2 TV speakers, you at least have the image near the center of the screen on one axis, which sort of gives you a "center of screen" acoustic image at a minimum. You won't have the wide-field only good properly spaced and raised mains can deliver (tweeter at listening position ear level for killer imaging). No time to run through the manual tonight, but hope should not be lost. WIll the experiment pay off? Maybe.
If you're on a budget like a lot of us, you can get great surround with relatively inexpensive speakers, sor less than 50 bucks each (shop and review). Grab a sub later. You've got a nice receiver with capabilities ready to go.
These tricks are used with high-end rigs, but the physics are the same, no matter the size or quality of speakers. Simply aligning mains and center speakers with the TV "screen center" as referenced above, PLUS time-aligning front-to back can produce an amazing sound-stage from inexpensive speakers. The center should be no exception, if possible. If the voice coils of the center and mains are placed aligned with the face of the TV/ monitor, the timing of the sound will originate at the image. And the tweeters aligned with screen center in height as well - all this will pay off big-time. The optimal listening position will be at at screen center. Also, be careful of time-smearing issues from reflective surfaces, especially the back wall, walls near speakers and floors. I've installed many "budget" systems with a very rewarding audio experience and also many high-end rigs (like mine) which are capable reproducing very accurate imaging across the entire sound spectrum, at realistic levels and at frequencies above and below human hearing(you feel it!). I even tune the speakers with EQ (your receiver) to the room for a flat response with a dedicated microphone and spectrum analyzer. Many A/V receivers are equipped with built-in version. The sky is the limit with A/V, but you've gotta start somewhere.