Without digging into the specifics of your existing kit, I expect the video is actually being transmitted as modem data over the POTS telephone link. Whether this data is a standard or non-standard modulation or format does not matter. What matters is that the modulated data stream gets from end to end without corruption.

Generally speaking, a cellular VOICE channel will not carry any signal other than speech. Data modulation (Modem chirps and tones) tend to get garbled by the cellular voice channel.

Even Fax, which is a fairly basic type of POTS modem data cannot be handled by cellular voice channels without specific provisions by the service provider.

If you want to communicate _data_ via a cellular link you need to utilize the data channel of the cellular service, which requires a data plan.

At the POTS end you need to somehow connect to the Internet, where in turn your connection from the cellular end would interconnect.