At the core of it all?

I wouldn't call it core on ET mostly due to the fact that it can be replaced by drums pretty easily.

Also are you saying that Phase Boots and Treads are not core items due to them being damage items?

I don't value Drums of Endurance anywhere near the amount I value Eul's on ET. Both are mobility enchancers, but even as a item to assist in Brawling and early fighting (Which is the point of early, Eul's is better on ET. Making Echo Stomp and Earth Splitter have some-what reliable set-up due to the spin changes the hero in game. Whilst yes, in an organised team, you can have a set-up stun lead into Echo Stomp, but Eul's is so versatle, and fits ET so well (Movement speed, mana sustain, a reliable disable to compensate for his lack of one). Where as Drum's, whilst cheaper and whilst it helps make you tanky, doesn't bring as much to the table through-out the game. But then I don't think Drums are that good for anything other than early Stats.

Eeeeh... Kinda? Like, I think Boots are generally one of the areas where the core item principle applies (Of it being situational), because almost every hero has a choice between 2 boots at a given point (Right Clickers want either generally Treads or Phase, non-right clickers generally want Tranquils or Arcanes. And I say generally, because I know there are exceptions, like Puck).

I don't really know what to think about boots in relation to being core items. I admit I didn't consider them earlier.... I'll say tht it's very rare for a single variety of boot to be core on a hero (I'd say Like a core Naga Siren and Tinker is an exception, because you'll build BOT's. Earthshaker as well, because you need the mana pool size just as much as the sustain). But there are usually two boots that are built more than the others on most heroes (A lot of heroes who build arcane boots can also get away with building Tranquils + Soul Ring instead)

then you havent seen the way euls is being used on ET.

You puny mortals, how can you compare drum which is essentially an overpriced point booster to the almighty Euls?

Euls -> Stomp = remove a hero from the game for 8 seconds.

Every hero is better with a Euls. Euls Gyro/Shadowfiend is a thing. So when you have a freaking 1.4 second delay stomp you just get dat Euls.

Euls doesn't work on ET in pubs because everyone would be so panic and right click everything.

Euls is for people who can use it.

When I play with friends at 3k mmr that's not the case anymore. At my current 2k though yes they tend to rightclick asap.

You gotta take that back.
I HAVE GAME SENSE.
If i ever see an ET on my team i dont touch the sleeping guys until its almost sure that the ulti will ht, then i go and nuke em up.
But yea i havent seen a euls ET anywhere on my skill level.
They just rely on his buffed stomp AoE.

Its a tricky question, I'd agree with most of the comments. There are very few truly "core" items - probably Boots of Travel on Tinker, Blink Dagger on Sand King, Magnus, Earthshaker etc.

Truly core items are ones which the heroes' playstyle depends very heavily on - i.e. they are much less effective without them.

All other "core" items are somewhat situational, but generally a very useful or safe choice. E.g. Aghanim's Scepter on Juggernaut, Boots of Speed on pretty much everyone, etc.

I'd also say core is somewhat time dependent - they're generally items you want to pick up fairly soon into the game, obviously carries have more flexibility here than supports.

Locket and KRdoto pretty much explained why Euls really isn't core on ET. You would actually need to be on a team with people who know what their doing for it to be successful.

Jakiro gets more use out of it due to him being able to dump all of his abilities right afterwards without a care.

While using Earth Splitter on one hero is somewhat of a waste.