They're probably ill-advised as they stand.
They obviously use Zen Archery as a precedent and zen archery (despite the misgivings I would probably have if it were proposed in an online forum rather than being printed in a book) hasn't caused any balance problems that I've observed yet. However, this is significantly different from zen archery for several reasons.
1. In order to be an effective archer, you need to have point blank, precise, and rapid shot. Consequently, any cleric constructed to take advantage of zen archery needed to be committed to archery from (basically) level 1. Since the cleric had to get to level 6 before he could get have all those feats and zen archery, he needed a decent stat in dexterity if he was to be effective in his chosen role during those levels.
Being effective in melee doesn't really require any feats--you can even get by wielding a morning star without power attack and cleave. So, there's no disadvantages built in to the construction of a character who ignores strength and then uses Zen melee to make up for the lack of strength in melee. Zen archery (as discussed before) has a built-in construction disadvantage since it's necessary to focus the character's early feats on archery.
2. Clerics are automatically proficient in good melee weapons but either need a war domain, favored weapon: bow god (Phaulkon is the only Greyhawk god like that) or to be elves (which means that they have to either have the (non-core) elf domain or wait until 9th level to have point blank shot, rapid shot, and zen archery--and that their dex bonus makes zen archery less attractive) in order to be proficient. This places further constraints upon the construction of the cleric-uber archer. (And you'll notice that most of the cleric archer builds on the boards don't feature zen archery--mostly for these reasons).
3. Monks aren't proficient with bows and rarely focus on ranged feats. Thus zen archery didn't really do much for monks. Zen Melee, OTOH, would be a must-have feat for monks.
However, that doesn't mean that such a feat would be wholly out of place.
The feat could probably be balanced by prerequisites. I'd suggest:
BAB +6, 5 ranks of Knowledge (Religion) or Knowledge (Arcana), Blindfight, Power attack.
Adding feats as prerequisites means that clerics need to make a significant feat commitment to melee before the level they take zen melee in order to be effective. Thus they face the same kind of constraints (although fewer) as the archer cleric.
Having Power attack as a feat prereq also smuggles in a 13+ strength requirement. (Combat Expertise would also be good and might perhaps make more sense in terms of flavor but expecting monks or clerics to have a 13+ int would make the feat less than useful in most 32 point buy or lower games). This immediately restricts the benefit from the feat (since the character will have a str bonus) and makes it less attractive to monks (who can't actually use power attack very well in 3.5 since their unarmed strikes are light weapons).
Blindfight was added to have a second feat and because the classic way to learn zen swordsmanship in movies seems to be training while blindfolded.
BAB +6 was added to further restrict the use of the feat. It's readily available to 9th level clerics and monks who have trained for it but extremely maximized builds will be rare since the character has to spend nearly half of their career without access to it (and needs to be effective enough to be fun playing until that point).