According to a few spec sites, the Tab4 7.0 doesn't have MHL output. According to Samsung's own site,
Samsung Galaxy ALPHA (Charcoal Black) - Wi-Fi, 12 MP, 4.7 HD Super AMOLED - Samsung UK , the Alpha doesn't either.
As far as [redacted], I can't see that you watch anything on it - it's a light controller.
You'll find out what Samsung says but if the phone has MHL capability, their own site is wrong.
(BTW, if you buy a Chromecast at Best Buy, you can return it until January 15 for a full refund if it doesn't do what you thought it would. Walmart also has a pretty liberal return policy - 10 or 15 days, I think.)
Hmmm - you may be in the UK, in which case those stores wouldn't apply (and the prices are in US dollars) but you should be able to find some holiday specials with decent return policies locally.