Very likely you can. You need to study the venting standards for the equipment as described in the installation manual until you understand them. I would guess that the method you want to use would be among those approved by the manufacturer. Who is going to install this equipment? If you don't understand it, you shouldn't do it. If you are going to have someone else install it, they should be able to show you the method of venting they are going to use and show you where in the manual that method is approved for installation.

Have you looked at pellet or corn, or multi-fuel stove? May save you a few bucks depending on the cost of gas in your area. If your set on gas, I'm not sure of what code requires. I would think as long as you have the proper vent pipe for gas you should be alright with existing routing.

After reading this entire posts and seeing no definitive answers, I'd figured I would chime in. As an architect I see a lot of projects where we replace an existing boiler with a Direct Vent (DV) boiler. 90% of the replacements use a horizontal, thru-wall vent. This is done typically because it is easier and less costly than going through a roof. Note on the attached link that there are maximum distances for vents and you are limited to where the outlets are in relation to windows, doors, A/C condensers, air intakes, overhangs, etc. You say you could use the 'unused, walled-in chimney' as a vertical vent. I assume this means a wood framed chimney enclosure. You could run PVC vent pipes vertically through this chimney but you would have a difficult time accessing the pipe joints and brackets during installation. DO NOT THINK ABOUT connecting to an old masonry chimney, even if it is terracotta lined. The direct vent gases are cool and will condense inside the chimney fast leaving a pool of highly corrosive water at the bottom of the chimney. This will eventually degrade the chimney and create possible CO leaks. For new construction I typically specify running the pipes vertically with a roof termination. This eliminates the steam plume shooting through the house wall while the boiler is on. Note that Weil McLain requires the pipes to slope back toward the boiler. I believe they collect the condensate and reheat it. Not certain how this works. I know that in a vertical installation there will be less vapor exhausted and more condensate generated as it rises through the pipe. This is typically collected at the bottom of the vertical stack into a condensate pump. This water is corrosive so be careful where it is pumped to (i.e. keep it away from landscaping). As long as you can find an inconspicuous location to vent the gases, the sidewall is the way to go for a retrofit. Here is a link that might be useful: Venting

You have an "attic insulation shield" in place now so insulation can go directly against that part, but not above it and contact the chimney pipe itself. I don't think a bit of air circulation is a bad thing around that flue. It would give more even temperatures along the pipe.