All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
First of all, it should be noted that in principle acts of worship can not be legislated without evidence from the Islamic legislation, otherwise they are not founded. Therefore, if these people have the habit of slaughtering in this way with the intention of worship, then this is not legislated, rather this could be included in what some scholars call "added innovations". Ash-Shaatibi said: 'Its criterion is to observe some specific modes and situations...or observing some acts of worship at special times which are not established by Islamic jurisprudence.'
Nonetheless, some slaughtering is not performed as an act of worship but rather as a habit, like slaughterg in order to eat meat or to feed a guest. Therefore, if the animals they slaughter are for the above purposes, (i.e. as a habit), then there is no harm in it, Allaah willing. However, this probability is unlikely here since the slaughtering is accompanied with the supplication, as this is evidence that their purpose is that they offer it as an act of worship.
Finally, it should be noted that the slaughtering on 'Eed Day, and the slaughtering on the occasion of a new born baby [Aqeeqah] are confirmed acts of the Prophet .
Allaah Knows best.