Chains were typically attached to collars worn by fantastic creatures, such as dragons and unicorns, etc., as a means of showing that they have been brought under man’s control.
I’ve also seen chains used to symbolize the bonds between members of a group. Lyon tends to use them in the corporate arms for Clan associations, Clan Campbell, for instance.
I suspect that there is some symbolic meaning to the armiger in the first example you posted, although it strikes me as odd. The second example seems to be more of an artistic design choice, although there is probably some symbolic meaning as well.
Sometimes the chain around a beast’s neck is supposed to signify that it can’t be controlled, shown by the opposite end of the chain not being attached to anything. I believe the Scottish unicorn is always depicted this way.
There are also chains of office (a decorative chain with a pendant in front worn over the shoulders), to which a chain in a coat of arms might conceivably allude.