What are the gameplay implications for each of the Digital Deluxe items?

I can't really speak for the elite skill's power. I assume though that it is on par with the other summon skills. It doesn't give an advantage to people with it, just another choice of elite skill. It's not necessarily a better one.

The miniature Rytlock is a cosmetic item: it will make a miniature character run after you. The miniature doesn't fight, and can't help you in any way.

The Golem Banker is a convenience item, allowing you a fast access to your bank, from almost any place in the game world. It's a consumable, usable only once. Once used, it lasts 5 days.

The Chalice of Glory is a one-time-use item giving 5000 of glory to your account. This allows you to buy cosmetic upgrades for your PvP weapons.

The Tome of Influence is also a one-time-use item which gives 1000 of Influence to the Guild you currently represent. Influence allows the guild to do research, and unlock guild services. Note that an equivalent to the tome of influence is earned through the game, the Letter of Commendation.

All in all, it doesn't really give a gameplay advantage over people with the normal edition. You just get items which are mostly convenient, or cosmetic.

Gnoupi's answer covered the items pretty well, so I'll talk a bit about the elite skill, Summon Mistfire Wolf.

Compared to other elites, Summon Mistfire Wolf is actually weaker. The closest analogue would be the Human elite Hounds of Balthazar. The Mistfire Wolf is slightly stronger than a single Hound of Balthazar, but the Hounds elite summons 2, plus the Hounds have a PBAoE attack.

The reason Summon Mistfire Wolf is weaker (in addition to the fact that it's a promo ability) is that unlike all the other elite skills, it unlocks automatically as soon as you reach level 30 and can use elites. The other elites have to be purchased for 10 or 30 skill points before they can be used.