They are not similar at all. It's not like any of the games you listed, actually.
In Demigod, you (mostly) control just your Demigod, of which you currently have 8 choices: fallen angel guy with crossbow (Regulus), nasty poison dog thing (Unclean Beast), the walking castle (Rook), undead mage (Torchbearer), walking suit of armor (Oak), evil plantsy/fairy thing (Queen of Thorns), girl on tiger (Sedna), and vampire (Lord Erebus).
The first 4 are classified as Assassins, they tend to have more damaging skills and direct damage.
The latter 4 are Generals, which tend to have more buffs and support skills, and in addition each General has their own unique minion type and they are able to buy 3 other minion types in a shop. These minions are the only things you can control like another strategy game. You can select them, tell them where to go and what to attack, etc. Assassins do not get minions at all.
The basic gameplay revolves around you controlling your lone Demigod (with minions if you're a General). There are AI "creeps" periodically coming out of the portals on both sides which you kill for experience, a little bit of gold. Of course, killing enemy Demigods gets you that too. With experience your Demigod levels up, and other than basic stats increases s/he becomes able to put skill points into the various skills available. For example, Regulus can put points in a Snipe skill (long range attack that does more damage the farther away the enemy is), Mines (throws some mines on the ground that blow up when something walks over them), Angelic Fury (adds damage to each crossbow shot but drains mana), Mark of Betrayer (puts a debuff on the enemy Demigod that causes them and all their allies nearby to take damage when they try to use a skill). Then there's passive skills, like longer range attack, chance to slow on each shot, chance to plant tracking bug that lets Regulus and his team see the tracked Demigod inside the fog of war, etc.
Each Demigod has unique skills, most of them have 4 active ones that you control the use of, and the rest are passive. Notable exceptions are Torchbearer and Queen of Thorns, they have 2 forms so they have 6 activated abilities (one slot is used for the form switch, so that leaves 3 per form). Torchbearer has Ice and Fire forms, Ice using interrupts and freezes and fire focusing on damage. Queen of Thorns has her "open flower" form which is more offensive with AoE attacks and such, and "closed flower" which gives her bonus armor and opens up her summoning and defensive skills.
There are a few different game modes, from killing x number of enemy Demigods to holding flags (flags exist in all game types though their numbers vary by different mode, and they provide bonuses while held such as extra xp gain, more health, faster health regen, etc) to destroying the enemy citadel.
There is no base building, your team's base comes "prebuilt" with a Citadel which you can buy upgrades for to improve towers (your irreplaceable defenses), your team's creeps, gold incomes, death penalty reduction, and unlock new creep types for reinforcements. Then there's a shop where you buy items to equip your Demigod, things like helms that increase mana regeneration, or chest armor that increases armor and life regeneration to boots that make you run faster or gloves that make you attack faster.
Things like that..