[Electronic M]

TV RF/IF circuits tend to be the more robust stages (tuners often need contact cleaning but it's a fairly easy fast job in most sets) Some Tube color sets were hotchassis(which can fry input sources and cause hum issues) and or didn't have good injection points for line level composite video and or audio. Don't open the direct audio/video injection can of worms till you have adaquately checked if the RF/IF system is ruined.

Assuming your old game console, DVD player or DTV tuner lack HDMI here's the set up you want...
TV connected thru 300 ohm (twin lead) to 75 ohm(Ftype coax) Balun, to a RF modulator, the modulator will take composite AV from an AV switch box. The AV switch box will take the composite output of all composite sources in your system and the output of your HDMI to composite converter. You will need an HDMI to composite converter too. If you plan on using more than 1 HDMI source device an HDMI switch to feed the HDMI to composite converter is nice to have.
EDIT: one nice option for an AV switch box is an old home theater amplifier they often can switch output by remote, and composite era ones are usually cheap. If you get lucky you might find a home theater amp that had composite and HDMI switches built in.

Until the TV restoration is completed I would focus on making a single signal source work rather than sinking money speculatively. If you have a test pattern disc a DVD player would be my choice for test mule signal source. If you don't have any other sets in your house that can tune analog RF I recommend getting an 11+ year old portable TV...they're small, should be new enough to still work and will tell you if your RF signal source chain is working.

The link you posted bumped my smartphone through several pages so I may not be looking at the right thing....But the device looks to only have HDMI and VGA inputs and outputs. VGA is at best a nightmare to directly inject in to a tube TV and at worst impossible to connect (it won't work if the VGA source device doesn't have a 640x480 resolution mode since tube era TVs won't accept the scan rate).