You haven't shown the leg arrangements, so a more immediate problem might be racking forces. That is, depending on how the legs are attached and arranged, a ~300lb. weight on the top may cause the entire table to swing like a pendulum and maybe even fold up where the legs meet the table.
However, it is my guess that, even at a nominal 1-inch thick, this table will eventually sag. Even if it doesn't, it might fall apart because of seasonal movement or flexing anyway.
Those joints are not going to be as strong as a nicely glued plank edge, even if you really sweat the details when gluing up and clamping. Expecting tongue and groove to support a span is unfair, as this is not what that joint is good at. Much of the gluing surface is missing, and in most cases there are going to be lots of voids where the tongue and groove doesn't quite mate for PVA glue to work its magic. And half those joints are going to be and grain on at least one of the pieces, which makes for a weaker joint.
So, it probably won't fall apart immediately, but I bet it'll keep flexing until some of the joints start to open up.
Note that, traditionally, tongue and groove surfaces were never intended to be glued anyway. They are a way to mate surfaces so they stay put, but still allow for seasonal movement. At most, you might blind-nail the edges together in a few places just to keep the joint tight to the material below it. If you glue these joints, the top might just pull itself apart by next year (depending on where you live.)
My advice would be to design a sturdy table using quality plywood (or solid wood, though plywood is hard to beat for its mass-to-strength ratio) then covering that with your solid wood "marquetry". Your edging will then hide that construction detail along with the raw edges of plywood.
Care would have to be take to make sure it is stiff enough for the static loads, and that the leg arrangement resists swaying when presented with racking forces. Sometimes you can combine leg attachments so that they offer both extra table stiffness along with racking strength. This is why I suggest you visit the previous Q&A on table design to get some ideas.
If you want to forego the plywood idea, I advise you experiment. Make a smaller version of your joinery top and see how it flexes under weight. Work tables useful for piling computers and equipment on top need to be able to hold up a medium sized person without cracking or flexing; you must be able to stand on it and not feel like it is going to fold up, or without hearing any ominous cracking sounds.
More specifically in your case, look at your design. Imagine your 300lb. static load right in the middle, at the joint where four pieces meet. These four joints are going to involve end-grain, and some of those joints the wood is going to want to move perpendicular to the grain (which often amounts to the same thing). My estimation of the failure mode is a crack starting at that corner, and then zig-zagging through any other of the joints to another point, where the stress pattern repeats.
When you lay flooring or bricks or wood siding, one of the important rules is to not have matching joints. That is, if you rotate your table top 45 degrees you'll see you have (essentially) 1x3 rectangles that your are combining to make a slab, but you are joining those 1x3 sections such that the joints are all along the same line. You are not using the strong glue joints to support the weaker wood joints. Thinking about the construction as a series of 1x3 sections you join together staggering the joints would go a long way toward getting an ideal slab strength.
We haven't even talked about material yet! You don't mention what sort of wood you want to use, or how well it is seasoned. But 10-inch squares are going to move, and they will move perpendicular to the grain. So, even if you carefully prep the mating surfaces and clamp ideally, after some time you might find that the top starts to buckle or crack.
If you used very stable and seasoned wood, and you carefully matched the grain so you minimized additive movement, and you glued up the top in sections ideally, staggering the joints, it might still move with seasonal changes.
In short, don't just focus on the top of a table build. Success relies on you getting a full idea of how static forces are handled through the top and transferred to the floor, but also how everyday use introduces dynamic forces that operate on completely different axes. The whole table needs to be designed to work together to give you the adequate strength in all these directions you need.
In conclusion, I don't want to suggest you give up the whole thing as a bad idea. I will point out that this is a very challenging project for the novice woodworker because you really have to know your material and your techniques.